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は，点 ",[20,1070,1072,1090],{"className":1071},[23],[20,1073,1075],{"className":1074},[27],[29,1076,1077],{"xmlns":31},[33,1078,1079,1087],{},[36,1080,1081,1083,1085],{},[39,1082,49],{},[43,1084,320],{},[39,1086,335],{},[54,1088,1089],{"encoding":56},"x = c",[20,1091,1093,1111],{"className":1092,"ariaHidden":62},[61],[20,1094,1096,1099,1102,1105,1108],{"className":1095},[66],[20,1097],{"className":1098,"style":665},[70],[20,1100,49],{"className":1101},[75,76],[20,1103],{"className":1104,"style":135},[134],[20,1106,320],{"className":1107},[139],[20,1109],{"className":1110,"style":135},[134],[20,1112,1114,1117],{"className":1113},[66],[20,1115],{"className":1116,"style":665},[70],[20,1118,335],{"className":1119},[75,76]," におけるグラフの接線の傾きを表す．",[16,1122,1123,1124,1127],{},"従って，この定理は「グラフが途切れることなく（連続），尖ったところがない（微分可能）なめらかな曲線であれば，",[678,1125,1126],{},"2点を通る直線と平行になるような接線が，その間のどこか（少なくとも1箇所）に必ず引ける","」ということを意味する．",{"title":1129,"searchDepth":1130,"depth":1130,"links":1131},"",2,[1132,1133],{"id":13,"depth":1130,"text":14},{"id":672,"depth":1130,"text":673},"定理",false,"md",{},true,"\u002Fdict\u002Faverage-th",{"title":6,"description":1129},"dict\u002Faverage-th\u002Findex","R_1xHEMXT7ayWXpulnPmCJZk8vIPlkWv2Qmiy6xCnfE","\u002Fcontent\u002Faverage-th",{"id":1145,"title":1146,"body":1147,"category":2809,"description":1129,"draft":1135,"extension":1136,"meta":2810,"navigation":1138,"path":2811,"seo":2812,"stem":2813,"__hash__":2814,"actualPath":2815},"dictionary\u002Fdict\u002Fderivative-function\u002Findex.md","導関数",{"type":8,"value":1148,"toc":2804},[1149,1153,1486,1808,2057,2061,2246,2250,2494],[11,1150,1152],{"id":1151},"_1-定義","1. 定義",[16,1154,18,1155,1224,1225,1253,1254,1282,1283,1360,1361,1438,1439,1482,1483,1485],{},[20,1156,1158,1183],{"className":1157},[23],[20,1159,1161],{"className":1160},[27],[29,1162,1163],{"xmlns":31},[33,1164,1165,1180],{},[36,1166,1167,1170,1172,1174,1176,1178],{},[39,1168,1169],{},"y",[43,1171,320],{},[39,1173,41],{},[43,1175,46],{"stretchy":45},[39,1177,49],{},[43,1179,52],{"stretchy":45},[54,1181,1182],{"encoding":56},"y=f(x)",[20,1184,1186,1206],{"className":1185,"ariaHidden":62},[61],[20,1187,1189,1193,1197,1200,1203],{"className":1188},[66],[20,1190],{"className":1191,"style":1192},[70],"height:0.625em;vertical-align:-0.1944em;",[20,1194,1169],{"className":1195,"style":1196},[75,76],"margin-right:0.0359em;",[20,1198],{"className":1199,"style":135},[134],[20,1201,320],{"className":1202},[139],[20,1204],{"className":1205,"style":135},[134],[20,1207,1209,1212,1215,1218,1221],{"className":1208},[66],[20,1210],{"className":1211,"style":71},[70],[20,1213,41],{"className":1214,"style":77},[75,76],[20,1216,46],{"className":1217},[81],[20,1219,49],{"className":1220},[75,76],[20,1222,52],{"className":1223},[88],"において，",[20,1226,1228,1241],{"className":1227},[23],[20,1229,1231],{"className":1230},[27],[29,1232,1233],{"xmlns":31},[33,1234,1235,1239],{},[36,1236,1237],{},[39,1238,49],{},[54,1240,49],{"encoding":56},[20,1242,1244],{"className":1243,"ariaHidden":62},[61],[20,1245,1247,1250],{"className":1246},[66],[20,1248],{"className":1249,"style":665},[70],[20,1251,49],{"className":1252},[75,76],"の値",[20,1255,1257,1270],{"className":1256},[23],[20,1258,1260],{"className":1259},[27],[29,1261,1262],{"xmlns":31},[33,1263,1264,1268],{},[36,1265,1266],{},[39,1267,104],{},[54,1269,104],{"encoding":56},[20,1271,1273],{"className":1272,"ariaHidden":62},[61],[20,1274,1276,1279],{"className":1275},[66],[20,1277],{"className":1278,"style":665},[70],[20,1280,104],{"className":1281},[75,76],"に微分係数",[20,1284,1286,1310],{"className":1285},[23],[20,1287,1289],{"className":1288},[27],[29,1290,1291],{"xmlns":31},[33,1292,1293,1307],{},[36,1294,1295,1301,1303,1305],{},[322,1296,1297,1299],{},[39,1298,41],{},[43,1300,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,1302,46],{"stretchy":45},[39,1304,104],{},[43,1306,52],{"stretchy":45},[54,1308,1309],{"encoding":56},"f'(a)",[20,1311,1313],{"className":1312,"ariaHidden":62},[61],[20,1314,1316,1319,1351,1354,1357],{"className":1315},[66],[20,1317],{"className":1318,"style":1026},[70],[20,1320,1322,1325],{"className":1321},[75],[20,1323,41],{"className":1324,"style":77},[75,76],[20,1326,1328],{"className":1327},[550],[20,1329,1331],{"className":1330},[396],[20,1332,1334],{"className":1333},[401],[20,1335,1337],{"className":1336,"style":560},[405],[20,1338,1339,1342],{"style":563},[20,1340],{"className":1341,"style":567},[413],[20,1343,1345],{"className":1344},[448,449,450,451],[20,1346,1348],{"className":1347},[75,451],[20,1349,330],{"className":1350},[75,451],[20,1352,46],{"className":1353},[81],[20,1355,104],{"className":1356},[75,76],[20,1358,52],{"className":1359},[88],"を対応させる関数",[20,1362,1364,1388],{"className":1363},[23],[20,1365,1367],{"className":1366},[27],[29,1368,1369],{"xmlns":31},[33,1370,1371,1385],{},[36,1372,1373,1379,1381,1383],{},[322,1374,1375,1377],{},[39,1376,41],{},[43,1378,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,1380,46],{"stretchy":45},[39,1382,49],{},[43,1384,52],{"stretchy":45},[54,1386,1387],{"encoding":56},"f'(x)",[20,1389,1391],{"className":1390,"ariaHidden":62},[61],[20,1392,1394,1397,1429,1432,1435],{"className":1393},[66],[20,1395],{"className":1396,"style":1026},[70],[20,1398,1400,1403],{"className":1399},[75],[20,1401,41],{"className":1402,"style":77},[75,76],[20,1404,1406],{"className":1405},[550],[20,1407,1409],{"className":1408},[396],[20,1410,1412],{"className":1411},[401],[20,1413,1415],{"className":1414,"style":560},[405],[20,1416,1417,1420],{"style":563},[20,1418],{"className":1419,"style":567},[413],[20,1421,1423],{"className":1422},[448,449,450,451],[20,1424,1426],{"className":1425},[75,451],[20,1427,330],{"className":1428},[75,451],[20,1430,46],{"className":1431},[81],[20,1433,49],{"className":1434},[75,76],[20,1436,52],{"className":1437},[88],"を，",[20,1440,1442,1461],{"className":1441},[23],[20,1443,1445],{"className":1444},[27],[29,1446,1447],{"xmlns":31},[33,1448,1449,1459],{},[36,1450,1451,1453,1455,1457],{},[39,1452,41],{},[43,1454,46],{"stretchy":45},[39,1456,49],{},[43,1458,52],{"stretchy":45},[54,1460,57],{"encoding":56},[20,1462,1464],{"className":1463,"ariaHidden":62},[61],[20,1465,1467,1470,1473,1476,1479],{"className":1466},[66],[20,1468],{"className":1469,"style":71},[70],[20,1471,41],{"className":1472,"style":77},[75,76],[20,1474,46],{"className":1475},[81],[20,1477,49],{"className":1478},[75,76],[20,1480,52],{"className":1481},[88],"の",[678,1484,1146],{},"と言う．",[20,1487,1489],{"className":1488},[251],[20,1490,1492,1569],{"className":1491},[23],[20,1493,1495],{"className":1494},[27],[29,1496,1497],{"xmlns":31,"display":260},[33,1498,1499,1566],{},[36,1500,1501,1507,1509,1511,1513,1515,1537],{},[322,1502,1503,1505],{},[39,1504,41],{},[43,1506,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,1508,46],{"stretchy":45},[39,1510,49],{},[43,1512,52],{"stretchy":45},[43,1514,320],{},[1516,1517,1518,1526],"munder",{},[36,1519,1520,1523],{},[39,1521,1522],{},"lim",[43,1524,1525],{},"⁡",[36,1527,1528,1531,1534],{},[39,1529,1530],{},"h",[43,1532,1533],{},"→",[1535,1536,283],"mn",{},[287,1538,1539,1564],{},[36,1540,1541,1543,1545,1547,1550,1552,1554,1556,1558,1560,1562],{},[39,1542,41],{},[43,1544,46],{"stretchy":45},[39,1546,49],{},[43,1548,1549],{},"+",[39,1551,1530],{},[43,1553,52],{"stretchy":45},[43,1555,301],{},[39,1557,41],{},[43,1559,46],{"stretchy":45},[39,1561,49],{},[43,1563,52],{"stretchy":45},[39,1565,1530],{},[54,1567,1568],{"encoding":56},"f'(x) = \\lim_{h \\to 0} \\frac{f(x+h)-f(x)}{h}",[20,1570,1572,1631],{"className":1571,"ariaHidden":62},[61],[20,1573,1575,1579,1613,1616,1619,1622,1625,1628],{"className":1574},[66],[20,1576],{"className":1577,"style":1578},[70],"height:1.0519em;vertical-align:-0.25em;",[20,1580,1582,1585],{"className":1581},[75],[20,1583,41],{"className":1584,"style":77},[75,76],[20,1586,1588],{"className":1587},[550],[20,1589,1591],{"className":1590},[396],[20,1592,1594],{"className":1593},[401],[20,1595,1598],{"className":1596,"style":1597},[405],"height:0.8019em;",[20,1599,1601,1604],{"style":1600},"top:-3.113em;margin-right:0.05em;",[20,1602],{"className":1603,"style":567},[413],[20,1605,1607],{"className":1606},[448,449,450,451],[20,1608,1610],{"className":1609},[75,451],[20,1611,330],{"className":1612},[75,451],[20,1614,46],{"className":1615},[81],[20,1617,49],{"className":1618},[75,76],[20,1620,52],{"className":1621},[88],[20,1623],{"className":1624,"style":135},[134],[20,1626,320],{"className":1627},[139],[20,1629],{"className":1630,"style":135},[134],[20,1632,1634,1638,1696,1699],{"className":1633},[66],[20,1635],{"className":1636,"style":1637},[70],"height:2.1791em;vertical-align:-0.7521em;",[20,1639,1643],{"className":1640},[1641,1642],"mop","op-limits",[20,1644,1646,1687],{"className":1645},[396,397],[20,1647,1649,1684],{"className":1648},[401],[20,1650,1652,1673],{"className":1651,"style":167},[405],[20,1653,1655,1658],{"style":1654},"top:-2.3479em;margin-left:0em;",[20,1656],{"className":1657,"style":444},[413],[20,1659,1661],{"className":1660},[448,449,450,451],[20,1662,1664,1667,1670],{"className":1663},[75,451],[20,1665,1530],{"className":1666},[75,76,451],[20,1668,1533],{"className":1669},[139,451],[20,1671,283],{"className":1672},[75,451],[20,1674,1676,1679],{"style":1675},"top:-3em;",[20,1677],{"className":1678,"style":444},[413],[20,1680,1681],{},[20,1682,1522],{"className":1683},[1641],[20,1685,519],{"className":1686},[518],[20,1688,1690],{"className":1689},[401],[20,1691,1694],{"className":1692,"style":1693},[405],"height:0.7521em;",[20,1695],{},[20,1697],{"className":1698,"style":904},[134],[20,1700,1702,1705,1805],{"className":1701},[75],[20,1703],{"className":1704},[81,424],[20,1706,1708],{"className":1707},[287],[20,1709,1711,1796],{"className":1710},[396,397],[20,1712,1714,1793],{"className":1713},[401],[20,1715,1718,1730,1738],{"className":1716,"style":1717},[405],"height:1.427em;",[20,1719,1721,1724],{"style":1720},"top:-2.314em;",[20,1722],{"className":1723,"style":444},[413],[20,1725,1727],{"className":1726},[75],[20,1728,1530],{"className":1729},[75,76],[20,1731,1732,1735],{"style":467},[20,1733],{"className":1734,"style":444},[413],[20,1736],{"className":1737,"style":475},[474],[20,1739,1741,1744],{"style":1740},"top:-3.677em;",[20,1742],{"className":1743,"style":444},[413],[20,1745,1747,1750,1753,1756,1760,1763,1766,1769,1772,1775,1778,1781,1784,1787,1790],{"className":1746},[75],[20,1748,41],{"className":1749,"style":77},[75,76],[20,1751,46],{"className":1752},[81],[20,1754,49],{"className":1755},[75,76],[20,1757],{"className":1758,"style":1759},[134],"margin-right:0.2222em;",[20,1761,1549],{"className":1762},[461],[20,1764],{"className":1765,"style":1759},[134],[20,1767,1530],{"className":1768},[75,76],[20,1770,52],{"className":1771},[88],[20,1773],{"className":1774,"style":1759},[134],[20,1776,301],{"className":1777},[461],[20,1779],{"className":1780,"style":1759},[134],[20,1782,41],{"className":1783,"style":77},[75,76],[20,1785,46],{"className":1786},[81],[20,1788,49],{"className":1789},[75,76],[20,1791,52],{"className":1792},[88],[20,1794,519],{"className":1795},[518],[20,1797,1799],{"className":1798},[401],[20,1800,1803],{"className":1801,"style":1802},[405],"height:0.686em;",[20,1804],{},[20,1806],{"className":1807},[88,424],[16,1809,1810,1838,1839,1867,1868,1896,1897,1838,1925,1867,2028,2056],{},[20,1811,1813,1826],{"className":1812},[23],[20,1814,1816],{"className":1815},[27],[29,1817,1818],{"xmlns":31},[33,1819,1820,1824],{},[36,1821,1822],{},[39,1823,49],{},[54,1825,49],{"encoding":56},[20,1827,1829],{"className":1828,"ariaHidden":62},[61],[20,1830,1832,1835],{"className":1831},[66],[20,1833],{"className":1834,"style":665},[70],[20,1836,49],{"className":1837},[75,76],"の値の変化量",[20,1840,1842,1855],{"className":1841},[23],[20,1843,1845],{"className":1844},[27],[29,1846,1847],{"xmlns":31},[33,1848,1849,1853],{},[36,1850,1851],{},[39,1852,1530],{},[54,1854,1530],{"encoding":56},[20,1856,1858],{"className":1857,"ariaHidden":62},[61],[20,1859,1861,1864],{"className":1860},[66],[20,1862],{"className":1863,"style":167},[70],[20,1865,1530],{"className":1866},[75,76],"を",[20,1869,1871,1884],{"className":1870},[23],[20,1872,1874],{"className":1873},[27],[29,1875,1876],{"xmlns":31},[33,1877,1878,1882],{},[36,1879,1880],{},[39,1881,49],{},[54,1883,49],{"encoding":56},[20,1885,1887],{"className":1886,"ariaHidden":62},[61],[20,1888,1890,1893],{"className":1889},[66],[20,1891],{"className":1892,"style":665},[70],[20,1894,49],{"className":1895},[75,76],"の増分，",[20,1898,1900,1913],{"className":1899},[23],[20,1901,1903],{"className":1902},[27],[29,1904,1905],{"xmlns":31},[33,1906,1907,1911],{},[36,1908,1909],{},[39,1910,1169],{},[54,1912,1169],{"encoding":56},[20,1914,1916],{"className":1915,"ariaHidden":62},[61],[20,1917,1919,1922],{"className":1918},[66],[20,1920],{"className":1921,"style":1192},[70],[20,1923,1169],{"className":1924,"style":1196},[75,76],[20,1926,1928,1962],{"className":1927},[23],[20,1929,1931],{"className":1930},[27],[29,1932,1933],{"xmlns":31},[33,1934,1935,1959],{},[36,1936,1937,1939,1941,1943,1945,1947,1949,1951,1953,1955,1957],{},[39,1938,41],{},[43,1940,46],{"stretchy":45},[39,1942,49],{},[43,1944,1549],{},[39,1946,1530],{},[43,1948,52],{"stretchy":45},[43,1950,301],{},[39,1952,41],{},[43,1954,46],{"stretchy":45},[39,1956,49],{},[43,1958,52],{"stretchy":45},[54,1960,1961],{"encoding":56},"f(x+h)-f(x)",[20,1963,1965,1989,2010],{"className":1964,"ariaHidden":62},[61],[20,1966,1968,1971,1974,1977,1980,1983,1986],{"className":1967},[66],[20,1969],{"className":1970,"style":71},[70],[20,1972,41],{"className":1973,"style":77},[75,76],[20,1975,46],{"className":1976},[81],[20,1978,49],{"className":1979},[75,76],[20,1981],{"className":1982,"style":1759},[134],[20,1984,1549],{"className":1985},[461],[20,1987],{"className":1988,"style":1759},[134],[20,1990,1992,1995,1998,2001,2004,2007],{"className":1991},[66],[20,1993],{"className":1994,"style":71},[70],[20,1996,1530],{"className":1997},[75,76],[20,1999,52],{"className":2000},[88],[20,2002],{"className":2003,"style":1759},[134],[20,2005,301],{"className":2006},[461],[20,2008],{"className":2009,"style":1759},[134],[20,2011,2013,2016,2019,2022,2025],{"className":2012},[66],[20,2014],{"className":2015,"style":71},[70],[20,2017,41],{"className":2018,"style":77},[75,76],[20,2020,46],{"className":2021},[81],[20,2023,49],{"className":2024},[75,76],[20,2026,52],{"className":2027},[88],[20,2029,2031,2044],{"className":2030},[23],[20,2032,2034],{"className":2033},[27],[29,2035,2036],{"xmlns":31},[33,2037,2038,2042],{},[36,2039,2040],{},[39,2041,1169],{},[54,2043,1169],{"encoding":56},[20,2045,2047],{"className":2046,"ariaHidden":62},[61],[20,2048,2050,2053],{"className":2049},[66],[20,2051],{"className":2052,"style":1192},[70],[20,2054,1169],{"className":2055,"style":1196},[75,76],"の増分という．",[11,2058,2060],{"id":2059},"_2-微分","2. 微分",[16,2062,2063,2091,2092,2135,2136,2212,2213,2241,2242,2245],{},[20,2064,2066,2079],{"className":2065},[23],[20,2067,2069],{"className":2068},[27],[29,2070,2071],{"xmlns":31},[33,2072,2073,2077],{},[36,2074,2075],{},[39,2076,49],{},[54,2078,49],{"encoding":56},[20,2080,2082],{"className":2081,"ariaHidden":62},[61],[20,2083,2085,2088],{"className":2084},[66],[20,2086],{"className":2087,"style":665},[70],[20,2089,49],{"className":2090},[75,76],"の関数",[20,2093,2095,2114],{"className":2094},[23],[20,2096,2098],{"className":2097},[27],[29,2099,2100],{"xmlns":31},[33,2101,2102,2112],{},[36,2103,2104,2106,2108,2110],{},[39,2105,41],{},[43,2107,46],{"stretchy":45},[39,2109,49],{},[43,2111,52],{"stretchy":45},[54,2113,57],{"encoding":56},[20,2115,2117],{"className":2116,"ariaHidden":62},[61],[20,2118,2120,2123,2126,2129,2132],{"className":2119},[66],[20,2121],{"className":2122,"style":71},[70],[20,2124,41],{"className":2125,"style":77},[75,76],[20,2127,46],{"className":2128},[81],[20,2130,49],{"className":2131},[75,76],[20,2133,52],{"className":2134},[88],"から導関数",[20,2137,2139,2162],{"className":2138},[23],[20,2140,2142],{"className":2141},[27],[29,2143,2144],{"xmlns":31},[33,2145,2146,2160],{},[36,2147,2148,2154,2156,2158],{},[322,2149,2150,2152],{},[39,2151,41],{},[43,2153,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,2155,46],{"stretchy":45},[39,2157,49],{},[43,2159,52],{"stretchy":45},[54,2161,1387],{"encoding":56},[20,2163,2165],{"className":2164,"ariaHidden":62},[61],[20,2166,2168,2171,2203,2206,2209],{"className":2167},[66],[20,2169],{"className":2170,"style":1026},[70],[20,2172,2174,2177],{"className":2173},[75],[20,2175,41],{"className":2176,"style":77},[75,76],[20,2178,2180],{"className":2179},[550],[20,2181,2183],{"className":2182},[396],[20,2184,2186],{"className":2185},[401],[20,2187,2189],{"className":2188,"style":560},[405],[20,2190,2191,2194],{"style":563},[20,2192],{"className":2193,"style":567},[413],[20,2195,2197],{"className":2196},[448,449,450,451],[20,2198,2200],{"className":2199},[75,451],[20,2201,330],{"className":2202},[75,451],[20,2204,46],{"className":2205},[81],[20,2207,49],{"className":2208},[75,76],[20,2210,52],{"className":2211},[88],"を求めることを，",[20,2214,2216,2229],{"className":2215},[23],[20,2217,2219],{"className":2218},[27],[29,2220,2221],{"xmlns":31},[33,2222,2223,2227],{},[36,2224,2225],{},[39,2226,49],{},[54,2228,49],{"encoding":56},[20,2230,2232],{"className":2231,"ariaHidden":62},[61],[20,2233,2235,2238],{"className":2234},[66],[20,2236],{"className":2237,"style":665},[70],[20,2239,49],{"className":2240},[75,76],"について",[678,2243,2244],{},"微分する","という．",[11,2247,2249],{"id":2248},"_3-導関数の性質","3. 導関数の性質",[16,2251,2252,2253,2283,2284,2355,2356],{},"(1) 定数",[20,2254,2256,2270],{"className":2255},[23],[20,2257,2259],{"className":2258},[27],[29,2260,2261],{"xmlns":31},[33,2262,2263,2268],{},[36,2264,2265],{},[39,2266,2267],{},"k",[54,2269,2267],{"encoding":56},[20,2271,2273],{"className":2272,"ariaHidden":62},[61],[20,2274,2276,2279],{"className":2275},[66],[20,2277],{"className":2278,"style":167},[70],[20,2280,2267],{"className":2281,"style":2282},[75,76],"margin-right:0.0315em;","について，",[20,2285,2287,2313],{"className":2286},[23],[20,2288,2290],{"className":2289},[27],[29,2291,2292],{"xmlns":31},[33,2293,2294,2310],{},[36,2295,2296,2298,2300,2302,2304,2306,2308],{},[39,2297,1169],{},[43,2299,320],{},[39,2301,2267],{},[39,2303,41],{},[43,2305,46],{"stretchy":45},[39,2307,49],{},[43,2309,52],{"stretchy":45},[54,2311,2312],{"encoding":56},"y=kf(x)",[20,2314,2316,2334],{"className":2315,"ariaHidden":62},[61],[20,2317,2319,2322,2325,2328,2331],{"className":2318},[66],[20,2320],{"className":2321,"style":1192},[70],[20,2323,1169],{"className":2324,"style":1196},[75,76],[20,2326],{"className":2327,"style":135},[134],[20,2329,320],{"className":2330},[139],[20,2332],{"className":2333,"style":135},[134],[20,2335,2337,2340,2343,2346,2349,2352],{"className":2336},[66],[20,2338],{"className":2339,"style":71},[70],[20,2341,2267],{"className":2342,"style":2282},[75,76],[20,2344,41],{"className":2345,"style":77},[75,76],[20,2347,46],{"className":2348},[81],[20,2350,49],{"className":2351},[75,76],[20,2353,52],{"className":2354},[88],"のとき，\n",[20,2357,2359,2393],{"className":2358},[23],[20,2360,2362],{"className":2361},[27],[29,2363,2364],{"xmlns":31},[33,2365,2366,2390],{},[36,2367,2368,2374,2376,2378,2384,2386,2388],{},[322,2369,2370,2372],{},[39,2371,1169],{},[43,2373,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,2375,320],{},[39,2377,2267],{},[322,2379,2380,2382],{},[39,2381,41],{},[43,2383,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,2385,46],{"stretchy":45},[39,2387,49],{},[43,2389,52],{"stretchy":45},[54,2391,2392],{"encoding":56},"    y' = k f'(x)\n   ",[20,2394,2396,2444],{"className":2395,"ariaHidden":62},[61],[20,2397,2399,2403,2435,2438,2441],{"className":2398},[66],[20,2400],{"className":2401,"style":2402},[70],"height:0.9463em;vertical-align:-0.1944em;",[20,2404,2406,2409],{"className":2405},[75],[20,2407,1169],{"className":2408,"style":1196},[75,76],[20,2410,2412],{"className":2411},[550],[20,2413,2415],{"className":2414},[396],[20,2416,2418],{"className":2417},[401],[20,2419,2421],{"className":2420,"style":560},[405],[20,2422,2423,2426],{"style":563},[20,2424],{"className":2425,"style":567},[413],[20,2427,2429],{"className":2428},[448,449,450,451],[20,2430,2432],{"className":2431},[75,451],[20,2433,330],{"className":2434},[75,451],[20,2436],{"className":2437,"style":135},[134],[20,2439,320],{"className":2440},[139],[20,2442],{"className":2443,"style":135},[134],[20,2445,2447,2450,2453,2485,2488,2491],{"className":2446},[66],[20,2448],{"className":2449,"style":1026},[70],[20,2451,2267],{"className":2452,"style":2282},[75,76],[20,2454,2456,2459],{"className":2455},[75],[20,2457,41],{"className":2458,"style":77},[75,76],[20,2460,2462],{"className":2461},[550],[20,2463,2465],{"className":2464},[396],[20,2466,2468],{"className":2467},[401],[20,2469,2471],{"className":2470,"style":560},[405],[20,2472,2473,2476],{"style":563},[20,2474],{"className":2475,"style":567},[413],[20,2477,2479],{"className":2478},[448,449,450,451],[20,2480,2482],{"className":2481},[75,451],[20,2483,330],{"className":2484},[75,451],[20,2486,46],{"className":2487},[81],[20,2489,49],{"className":2490},[75,76],[20,2492,52],{"className":2493},[88],[16,2495,2496,2497,2355,2602],{},"(2) ",[20,2498,2500,2536],{"className":2499},[23],[20,2501,2503],{"className":2502},[27],[29,2504,2505],{"xmlns":31},[33,2506,2507,2533],{},[36,2508,2509,2511,2513,2515,2517,2519,2521,2524,2527,2529,2531],{},[39,2510,1169],{},[43,2512,320],{},[39,2514,41],{},[43,2516,46],{"stretchy":45},[39,2518,49],{},[43,2520,52],{"stretchy":45},[43,2522,2523],{},"±",[39,2525,2526],{},"g",[43,2528,46],{"stretchy":45},[39,2530,49],{},[43,2532,52],{"stretchy":45},[54,2534,2535],{"encoding":56},"y=f(x) \\pm g(x)",[20,2537,2539,2557,2584],{"className":2538,"ariaHidden":62},[61],[20,2540,2542,2545,2548,2551,2554],{"className":2541},[66],[20,2543],{"className":2544,"style":1192},[70],[20,2546,1169],{"className":2547,"style":1196},[75,76],[20,2549],{"className":2550,"style":135},[134],[20,2552,320],{"className":2553},[139],[20,2555],{"className":2556,"style":135},[134],[20,2558,2560,2563,2566,2569,2572,2575,2578,2581],{"className":2559},[66],[20,2561],{"className":2562,"style":71},[70],[20,2564,41],{"className":2565,"style":77},[75,76],[20,2567,46],{"className":2568},[81],[20,2570,49],{"className":2571},[75,76],[20,2573,52],{"className":2574},[88],[20,2576],{"className":2577,"style":1759},[134],[20,2579,2523],{"className":2580},[461],[20,2582],{"className":2583,"style":1759},[134],[20,2585,2587,2590,2593,2596,2599],{"className":2586},[66],[20,2588],{"className":2589,"style":71},[70],[20,2591,2526],{"className":2592,"style":1196},[75,76],[20,2594,46],{"className":2595},[81],[20,2597,49],{"className":2598},[75,76],[20,2600,52],{"className":2601},[88],[20,2603,2605,2651],{"className":2604},[23],[20,2606,2608],{"className":2607},[27],[29,2609,2610],{"xmlns":31},[33,2611,2612,2648],{},[36,2613,2614,2620,2622,2628,2630,2632,2634,2636,2642,2644,2646],{},[322,2615,2616,2618],{},[39,2617,1169],{},[43,2619,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,2621,320],{},[322,2623,2624,2626],{},[39,2625,41],{},[43,2627,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,2629,46],{"stretchy":45},[39,2631,49],{},[43,2633,52],{"stretchy":45},[43,2635,2523],{},[322,2637,2638,2640],{},[39,2639,2526],{},[43,2641,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,2643,46],{"stretchy":45},[39,2645,49],{},[43,2647,52],{"stretchy":45},[54,2649,2650],{"encoding":56},"    y' = f'(x) \\pm g'(x)\n   ",[20,2652,2654,2701,2757],{"className":2653,"ariaHidden":62},[61],[20,2655,2657,2660,2692,2695,2698],{"className":2656},[66],[20,2658],{"className":2659,"style":2402},[70],[20,2661,2663,2666],{"className":2662},[75],[20,2664,1169],{"className":2665,"style":1196},[75,76],[20,2667,2669],{"className":2668},[550],[20,2670,2672],{"className":2671},[396],[20,2673,2675],{"className":2674},[401],[20,2676,2678],{"className":2677,"style":560},[405],[20,2679,2680,2683],{"style":563},[20,2681],{"className":2682,"style":567},[413],[20,2684,2686],{"className":2685},[448,449,450,451],[20,2687,2689],{"className":2688},[75,451],[20,2690,330],{"className":2691},[75,451],[20,2693],{"className":2694,"style":135},[134],[20,2696,320],{"className":2697},[139],[20,2699],{"className":2700,"style":135},[134],[20,2702,2704,2707,2739,2742,2745,2748,2751,2754],{"className":2703},[66],[20,2705],{"className":2706,"style":1026},[70],[20,2708,2710,2713],{"className":2709},[75],[20,2711,41],{"className":2712,"style":77},[75,76],[20,2714,2716],{"className":2715},[550],[20,2717,2719],{"className":2718},[396],[20,2720,2722],{"className":2721},[401],[20,2723,2725],{"className":2724,"style":560},[405],[20,2726,2727,2730],{"style":563},[20,2728],{"className":2729,"style":567},[413],[20,2731,2733],{"className":2732},[448,449,450,451],[20,2734,2736],{"className":2735},[75,451],[20,2737,330],{"className":2738},[75,451],[20,2740,46],{"className":2741},[81],[20,2743,49],{"className":2744},[75,76],[20,2746,52],{"className":2747},[88],[20,2749],{"className":2750,"style":1759},[134],[20,2752,2523],{"className":2753},[461],[20,2755],{"className":2756,"style":1759},[134],[20,2758,2760,2763,2795,2798,2801],{"className":2759},[66],[20,2761],{"className":2762,"style":1026},[70],[20,2764,2766,2769],{"className":2765},[75],[20,2767,2526],{"className":2768,"style":1196},[75,76],[20,2770,2772],{"className":2771},[550],[20,2773,2775],{"className":2774},[396],[20,2776,2778],{"className":2777},[401],[20,2779,2781],{"className":2780,"style":560},[405],[20,2782,2783,2786],{"style":563},[20,2784],{"className":2785,"style":567},[413],[20,2787,2789],{"className":2788},[448,449,450,451],[20,2790,2792],{"className":2791},[75,451],[20,2793,330],{"className":2794},[75,451],[20,2796,46],{"className":2797},[81],[20,2799,49],{"className":2800},[75,76],[20,2802,52],{"className":2803},[88],{"title":1129,"searchDepth":1130,"depth":1130,"links":2805},[2806,2807,2808],{"id":1151,"depth":1130,"text":1152},{"id":2059,"depth":1130,"text":2060},{"id":2248,"depth":1130,"text":2249},"定義",{},"\u002Fdict\u002Fderivative-function",{"title":1146,"description":1129},"dict\u002Fderivative-function\u002Findex","GSbjDc8uAwBhQ7c-z5Oa-KeSp8j_mzcHI8CdLHO3x4Y","\u002Fcontent\u002Fderivative-function",{"id":2817,"title":2818,"body":2819,"category":2809,"description":1129,"draft":1135,"extension":1136,"meta":5235,"navigation":1138,"path":5236,"seo":5237,"stem":5238,"__hash__":5239,"actualPath":5240},"dictionary\u002Fdict\u002Fdifferential-coefficient\u002Findex.md","微分係数",{"type":8,"value":2820,"toc":5227},[2821,2825,2828,2832,2911,3218,3221,3522,3526,3656,3923,4308,4485,4630,4882,4887,4950],[11,2822,2824],{"id":2823},"_1-概要","1. 概要",[16,2826,2827],{},"ある関数の特定の一点における，瞬間の変化率（グラフの場合接線の傾き）を示す．",[11,2829,2831],{"id":2830},"_2-定義","2. 定義",[16,2833,2818,2834,2910],{},[20,2835,2837,2860],{"className":2836},[23],[20,2838,2840],{"className":2839},[27],[29,2841,2842],{"xmlns":31},[33,2843,2844,2858],{},[36,2845,2846,2852,2854,2856],{},[322,2847,2848,2850],{},[39,2849,41],{},[43,2851,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,2853,46],{"stretchy":45},[39,2855,104],{},[43,2857,52],{"stretchy":45},[54,2859,1309],{"encoding":56},[20,2861,2863],{"className":2862,"ariaHidden":62},[61],[20,2864,2866,2869,2901,2904,2907],{"className":2865},[66],[20,2867],{"className":2868,"style":1026},[70],[20,2870,2872,2875],{"className":2871},[75],[20,2873,41],{"className":2874,"style":77},[75,76],[20,2876,2878],{"className":2877},[550],[20,2879,2881],{"className":2880},[396],[20,2882,2884],{"className":2883},[401],[20,2885,2887],{"className":2886,"style":560},[405],[20,2888,2889,2892],{"style":563},[20,2890],{"className":2891,"style":567},[413],[20,2893,2895],{"className":2894},[448,449,450,451],[20,2896,2898],{"className":2897},[75,451],[20,2899,330],{"className":2900},[75,451],[20,2902,46],{"className":2903},[81],[20,2905,104],{"className":2906},[75,76],[20,2908,52],{"className":2909},[88],"が存在するとき，",[20,2912,2914],{"className":2913},[251],[20,2915,2917,2989],{"className":2916},[23],[20,2918,2920],{"className":2919},[27],[29,2921,2922],{"xmlns":31,"display":260},[33,2923,2924,2986],{},[36,2925,2926,2942,2972,2974,2980,2982,2984],{},[1516,2927,2928,2934],{},[36,2929,2930,2932],{},[39,2931,1522],{},[43,2933,1525],{},[36,2935,2936,2938,2940],{},[39,2937,49],{},[43,2939,1533],{},[39,2941,104],{},[287,2943,2944,2964],{},[36,2945,2946,2948,2950,2952,2954,2956,2958,2960,2962],{},[39,2947,41],{},[43,2949,46],{"stretchy":45},[39,2951,49],{},[43,2953,52],{"stretchy":45},[43,2955,301],{},[39,2957,41],{},[43,2959,46],{"stretchy":45},[39,2961,104],{},[43,2963,52],{"stretchy":45},[36,2965,2966,2968,2970],{},[39,2967,49],{},[43,2969,301],{},[39,2971,104],{},[43,2973,320],{},[322,2975,2976,2978],{},[39,2977,41],{},[43,2979,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,2981,46],{"stretchy":45},[39,2983,104],{},[43,2985,52],{"stretchy":45},[54,2987,2988],{"encoding":56},"\\lim_{x \\to a} \\frac{f(x) - f(a)}{x-a} = f'(a)",[20,2990,2992,3171],{"className":2991,"ariaHidden":62},[61],[20,2993,2995,2999,3054,3057,3162,3165,3168],{"className":2994},[66],[20,2996],{"className":2997,"style":2998},[70],"height:2.1963em;vertical-align:-0.7693em;",[20,3000,3002],{"className":3001},[1641,1642],[20,3003,3005,3045],{"className":3004},[396,397],[20,3006,3008,3042],{"className":3007},[401],[20,3009,3011,3032],{"className":3010,"style":167},[405],[20,3012,3014,3017],{"style":3013},"top:-2.4em;margin-left:0em;",[20,3015],{"className":3016,"style":444},[413],[20,3018,3020],{"className":3019},[448,449,450,451],[20,3021,3023,3026,3029],{"className":3022},[75,451],[20,3024,49],{"className":3025},[75,76,451],[20,3027,1533],{"className":3028},[139,451],[20,3030,104],{"className":3031},[75,76,451],[20,3033,3034,3037],{"style":1675},[20,3035],{"className":3036,"style":444},[413],[20,3038,3039],{},[20,3040,1522],{"className":3041},[1641],[20,3043,519],{"className":3044},[518],[20,3046,3048],{"className":3047},[401],[20,3049,3052],{"className":3050,"style":3051},[405],"height:0.7em;",[20,3053],{},[20,3055],{"className":3056,"style":904},[134],[20,3058,3060,3063,3159],{"className":3059},[75],[20,3061],{"className":3062},[81,424],[20,3064,3066],{"className":3065},[287],[20,3067,3069,3150],{"className":3068},[396,397],[20,3070,3072,3147],{"className":3071},[401],[20,3073,3075,3098,3106],{"className":3074,"style":1717},[405],[20,3076,3077,3080],{"style":1720},[20,3078],{"className":3079,"style":444},[413],[20,3081,3083,3086,3089,3092,3095],{"className":3082},[75],[20,3084,49],{"className":3085},[75,76],[20,3087],{"className":3088,"style":1759},[134],[20,3090,301],{"className":3091},[461],[20,3093],{"className":3094,"style":1759},[134],[20,3096,104],{"className":3097},[75,76],[20,3099,3100,3103],{"style":467},[20,3101],{"className":3102,"style":444},[413],[20,3104],{"className":3105,"style":475},[474],[20,3107,3108,3111],{"style":1740},[20,3109],{"className":3110,"style":444},[413],[20,3112,3114,3117,3120,3123,3126,3129,3132,3135,3138,3141,3144],{"className":3113},[75],[20,3115,41],{"className":3116,"style":77},[75,76],[20,3118,46],{"className":3119},[81],[20,3121,49],{"className":3122},[75,76],[20,3124,52],{"className":3125},[88],[20,3127],{"className":3128,"style":1759},[134],[20,3130,301],{"className":3131},[461],[20,3133],{"className":3134,"style":1759},[134],[20,3136,41],{"className":3137,"style":77},[75,76],[20,3139,46],{"className":3140},[81],[20,3142,104],{"className":3143},[75,76],[20,3145,52],{"className":3146},[88],[20,3148,519],{"className":3149},[518],[20,3151,3153],{"className":3152},[401],[20,3154,3157],{"className":3155,"style":3156},[405],"height:0.7693em;",[20,3158],{},[20,3160],{"className":3161},[88,424],[20,3163],{"className":3164,"style":135},[134],[20,3166,320],{"className":3167},[139],[20,3169],{"className":3170,"style":135},[134],[20,3172,3174,3177,3209,3212,3215],{"className":3173},[66],[20,3175],{"className":3176,"style":1578},[70],[20,3178,3180,3183],{"className":3179},[75],[20,3181,41],{"className":3182,"style":77},[75,76],[20,3184,3186],{"className":3185},[550],[20,3187,3189],{"className":3188},[396],[20,3190,3192],{"className":3191},[401],[20,3193,3195],{"className":3194,"style":1597},[405],[20,3196,3197,3200],{"style":1600},[20,3198],{"className":3199,"style":567},[413],[20,3201,3203],{"className":3202},[448,449,450,451],[20,3204,3206],{"className":3205},[75,451],[20,3207,330],{"className":3208},[75,451],[20,3210,46],{"className":3211},[81],[20,3213,104],{"className":3214},[75,76],[20,3216,52],{"className":3217},[88],[16,3219,3220],{},"または",[20,3222,3224],{"className":3223},[251],[20,3225,3227,3297],{"className":3226},[23],[20,3228,3230],{"className":3229},[27],[29,3231,3232],{"xmlns":31,"display":260},[33,3233,3234,3294],{},[36,3235,3236,3252,3280,3282,3288,3290,3292],{},[1516,3237,3238,3244],{},[36,3239,3240,3242],{},[39,3241,1522],{},[43,3243,1525],{},[36,3245,3246,3248,3250],{},[39,3247,1530],{},[43,3249,1533],{},[1535,3251,283],{},[287,3253,3254,3278],{},[36,3255,3256,3258,3260,3262,3264,3266,3268,3270,3272,3274,3276],{},[39,3257,41],{},[43,3259,46],{"stretchy":45},[39,3261,104],{},[43,3263,1549],{},[39,3265,1530],{},[43,3267,52],{"stretchy":45},[43,3269,301],{},[39,3271,41],{},[43,3273,46],{"stretchy":45},[39,3275,104],{},[43,3277,52],{"stretchy":45},[39,3279,1530],{},[43,3281,320],{},[322,3283,3284,3286],{},[39,3285,41],{},[43,3287,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,3289,46],{"stretchy":45},[39,3291,104],{},[43,3293,52],{"stretchy":45},[54,3295,3296],{"encoding":56},"\\lim_{h \\to 0} \\frac{f(a + h) - f(a)}{h} = f'(a)",[20,3298,3300,3475],{"className":3299,"ariaHidden":62},[61],[20,3301,3303,3306,3359,3362,3466,3469,3472],{"className":3302},[66],[20,3304],{"className":3305,"style":1637},[70],[20,3307,3309],{"className":3308},[1641,1642],[20,3310,3312,3351],{"className":3311},[396,397],[20,3313,3315,3348],{"className":3314},[401],[20,3316,3318,3338],{"className":3317,"style":167},[405],[20,3319,3320,3323],{"style":1654},[20,3321],{"className":3322,"style":444},[413],[20,3324,3326],{"className":3325},[448,449,450,451],[20,3327,3329,3332,3335],{"className":3328},[75,451],[20,3330,1530],{"className":3331},[75,76,451],[20,3333,1533],{"className":3334},[139,451],[20,3336,283],{"className":3337},[75,451],[20,3339,3340,3343],{"style":1675},[20,3341],{"className":3342,"style":444},[413],[20,3344,3345],{},[20,3346,1522],{"className":3347},[1641],[20,3349,519],{"className":3350},[518],[20,3352,3354],{"className":3353},[401],[20,3355,3357],{"className":3356,"style":1693},[405],[20,3358],{},[20,3360],{"className":3361,"style":904},[134],[20,3363,3365,3368,3463],{"className":3364},[75],[20,3366],{"className":3367},[81,424],[20,3369,3371],{"className":3370},[287],[20,3372,3374,3455],{"className":3373},[396,397],[20,3375,3377,3452],{"className":3376},[401],[20,3378,3380,3391,3399],{"className":3379,"style":1717},[405],[20,3381,3382,3385],{"style":1720},[20,3383],{"className":3384,"style":444},[413],[20,3386,3388],{"className":3387},[75],[20,3389,1530],{"className":3390},[75,76],[20,3392,3393,3396],{"style":467},[20,3394],{"className":3395,"style":444},[413],[20,3397],{"className":3398,"style":475},[474],[20,3400,3401,3404],{"style":1740},[20,3402],{"className":3403,"style":444},[413],[20,3405,3407,3410,3413,3416,3419,3422,3425,3428,3431,3434,3437,3440,3443,3446,3449],{"className":3406},[75],[20,3408,41],{"className":3409,"style":77},[75,76],[20,3411,46],{"className":3412},[81],[20,3414,104],{"className":3415},[75,76],[20,3417],{"className":3418,"style":1759},[134],[20,3420,1549],{"className":3421},[461],[20,3423],{"className":3424,"style":1759},[134],[20,3426,1530],{"className":3427},[75,76],[20,3429,52],{"className":3430},[88],[20,3432],{"className":3433,"style":1759},[134],[20,3435,301],{"className":3436},[461],[20,3438],{"className":3439,"style":1759},[134],[20,3441,41],{"className":3442,"style":77},[75,76],[20,3444,46],{"className":3445},[81],[20,3447,104],{"className":3448},[75,76],[20,3450,52],{"className":3451},[88],[20,3453,519],{"className":3454},[518],[20,3456,3458],{"className":3457},[401],[20,3459,3461],{"className":3460,"style":1802},[405],[20,3462],{},[20,3464],{"className":3465},[88,424],[20,3467],{"className":3468,"style":135},[134],[20,3470,320],{"className":3471},[139],[20,3473],{"className":3474,"style":135},[134],[20,3476,3478,3481,3513,3516,3519],{"className":3477},[66],[20,3479],{"className":3480,"style":1578},[70],[20,3482,3484,3487],{"className":3483},[75],[20,3485,41],{"className":3486,"style":77},[75,76],[20,3488,3490],{"className":3489},[550],[20,3491,3493],{"className":3492},[396],[20,3494,3496],{"className":3495},[401],[20,3497,3499],{"className":3498,"style":1597},[405],[20,3500,3501,3504],{"style":1600},[20,3502],{"className":3503,"style":567},[413],[20,3505,3507],{"className":3506},[448,449,450,451],[20,3508,3510],{"className":3509},[75,451],[20,3511,330],{"className":3512},[75,451],[20,3514,46],{"className":3515},[81],[20,3517,104],{"className":3518},[75,76],[20,3520,52],{"className":3521},[88],[11,3523,3525],{"id":3524},"_3-図形的性質","3. 図形的性質",[16,3527,3528,3529,3580,3581,3655],{},"微分係数は",[20,3530,3532,3550],{"className":3531},[23],[20,3533,3535],{"className":3534},[27],[29,3536,3537],{"xmlns":31},[33,3538,3539,3547],{},[36,3540,3541,3543,3545],{},[39,3542,49],{},[43,3544,320],{},[39,3546,104],{},[54,3548,3549],{"encoding":56},"x=a",[20,3551,3553,3571],{"className":3552,"ariaHidden":62},[61],[20,3554,3556,3559,3562,3565,3568],{"className":3555},[66],[20,3557],{"className":3558,"style":665},[70],[20,3560,49],{"className":3561},[75,76],[20,3563],{"className":3564,"style":135},[134],[20,3566,320],{"className":3567},[139],[20,3569],{"className":3570,"style":135},[134],[20,3572,3574,3577],{"className":3573},[66],[20,3575],{"className":3576,"style":665},[70],[20,3578,104],{"className":3579},[75,76],"から",[20,3582,3584,3606],{"className":3583},[23],[20,3585,3587],{"className":3586},[27],[29,3588,3589],{"xmlns":31},[33,3590,3591,3603],{},[36,3592,3593,3595,3597,3599,3601],{},[39,3594,49],{},[43,3596,320],{},[39,3598,104],{},[43,3600,1549],{},[39,3602,1530],{},[54,3604,3605],{"encoding":56},"x=a+h",[20,3607,3609,3627,3646],{"className":3608,"ariaHidden":62},[61],[20,3610,3612,3615,3618,3621,3624],{"className":3611},[66],[20,3613],{"className":3614,"style":665},[70],[20,3616,49],{"className":3617},[75,76],[20,3619],{"className":3620,"style":135},[134],[20,3622,320],{"className":3623},[139],[20,3625],{"className":3626,"style":135},[134],[20,3628,3630,3634,3637,3640,3643],{"className":3629},[66],[20,3631],{"className":3632,"style":3633},[70],"height:0.6667em;vertical-align:-0.0833em;",[20,3635,104],{"className":3636},[75,76],[20,3638],{"className":3639,"style":1759},[134],[20,3641,1549],{"className":3642},[461],[20,3644],{"className":3645,"style":1759},[134],[20,3647,3649,3652],{"className":3648},[66],[20,3650],{"className":3651,"style":167},[70],[20,3653,1530],{"className":3654},[75,76],"までの平均変化率を用いて，",[20,3657,3659],{"className":3658},[251],[20,3660,3662,3726],{"className":3661},[23],[20,3663,3665],{"className":3664},[27],[29,3666,3667],{"xmlns":31,"display":260},[33,3668,3669,3723],{},[36,3670,3671,3699,3701,3707,3709,3711,3713,3715,3717,3719,3721],{},[287,3672,3673,3697],{},[36,3674,3675,3677,3679,3681,3683,3685,3687,3689,3691,3693,3695],{},[39,3676,41],{},[43,3678,46],{"stretchy":45},[39,3680,104],{},[43,3682,1549],{},[39,3684,1530],{},[43,3686,52],{"stretchy":45},[43,3688,301],{},[39,3690,41],{},[43,3692,46],{"stretchy":45},[39,3694,104],{},[43,3696,52],{"stretchy":45},[39,3698,1530],{},[43,3700,1533],{},[322,3702,3703,3705],{},[39,3704,41],{},[43,3706,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,3708,46],{"stretchy":45},[39,3710,104],{},[43,3712,52],{"stretchy":45},[43,3714,46],{"stretchy":45},[39,3716,1530],{},[43,3718,1533],{},[1535,3720,283],{},[43,3722,52],{"stretchy":45},[54,3724,3725],{"encoding":56},"\\frac{f(a+h)-f(a)}{h} \\to f'(a) (h \\to 0)",[20,3727,3729,3849,3911],{"className":3728,"ariaHidden":62},[61],[20,3730,3732,3736,3840,3843,3846],{"className":3731},[66],[20,3733],{"className":3734,"style":3735},[70],"height:2.113em;vertical-align:-0.686em;",[20,3737,3739,3742,3837],{"className":3738},[75],[20,3740],{"className":3741},[81,424],[20,3743,3745],{"className":3744},[287],[20,3746,3748,3829],{"className":3747},[396,397],[20,3749,3751,3826],{"className":3750},[401],[20,3752,3754,3765,3773],{"className":3753,"style":1717},[405],[20,3755,3756,3759],{"style":1720},[20,3757],{"className":3758,"style":444},[413],[20,3760,3762],{"className":3761},[75],[20,3763,1530],{"className":3764},[75,76],[20,3766,3767,3770],{"style":467},[20,3768],{"className":3769,"style":444},[413],[20,3771],{"className":3772,"style":475},[474],[20,3774,3775,3778],{"style":1740},[20,3776],{"className":3777,"style":444},[413],[20,3779,3781,3784,3787,3790,3793,3796,3799,3802,3805,3808,3811,3814,3817,3820,3823],{"className":3780},[75],[20,3782,41],{"className":3783,"style":77},[75,76],[20,3785,46],{"className":3786},[81],[20,3788,104],{"className":3789},[75,76],[20,3791],{"className":3792,"style":1759},[134],[20,3794,1549],{"className":3795},[461],[20,3797],{"className":3798,"style":1759},[134],[20,3800,1530],{"className":3801},[75,76],[20,3803,52],{"className":3804},[88],[20,3806],{"className":3807,"style":1759},[134],[20,3809,301],{"className":3810},[461],[20,3812],{"className":3813,"style":1759},[134],[20,3815,41],{"className":3816,"style":77},[75,76],[20,3818,46],{"className":3819},[81],[20,3821,104],{"className":3822},[75,76],[20,3824,52],{"className":3825},[88],[20,3827,519],{"className":3828},[518],[20,3830,3832],{"className":3831},[401],[20,3833,3835],{"className":3834,"style":1802},[405],[20,3836],{},[20,3838],{"className":3839},[88,424],[20,3841],{"className":3842,"style":135},[134],[20,3844,1533],{"className":3845},[139],[20,3847],{"className":3848,"style":135},[134],[20,3850,3852,3855,3887,3890,3893,3896,3899,3902,3905,3908],{"className":3851},[66],[20,3853],{"className":3854,"style":1578},[70],[20,3856,3858,3861],{"className":3857},[75],[20,3859,41],{"className":3860,"style":77},[75,76],[20,3862,3864],{"className":3863},[550],[20,3865,3867],{"className":3866},[396],[20,3868,3870],{"className":3869},[401],[20,3871,3873],{"className":3872,"style":1597},[405],[20,3874,3875,3878],{"style":1600},[20,3876],{"className":3877,"style":567},[413],[20,3879,3881],{"className":3880},[448,449,450,451],[20,3882,3884],{"className":3883},[75,451],[20,3885,330],{"className":3886},[75,451],[20,3888,46],{"className":3889},[81],[20,3891,104],{"className":3892},[75,76],[20,3894,52],{"className":3895},[88],[20,3897,46],{"className":3898},[81],[20,3900,1530],{"className":3901},[75,76],[20,3903],{"className":3904,"style":135},[134],[20,3906,1533],{"className":3907},[139],[20,3909],{"className":3910,"style":135},[134],[20,3912,3914,3917,3920],{"className":3913},[66],[20,3915],{"className":3916,"style":71},[70],[20,3918,283],{"className":3919},[75],[20,3921,52],{"className":3922},[88],[16,3924,3925,3926,1482,3991,4041,4042,4118,4119,4147,4148,4177,4178,4243,4244,4307],{},"であるから，関数",[20,3927,3929,3952],{"className":3928},[23],[20,3930,3932],{"className":3931},[27],[29,3933,3934],{"xmlns":31},[33,3935,3936,3950],{},[36,3937,3938,3940,3942,3944,3946,3948],{},[39,3939,1169],{},[43,3941,320],{},[39,3943,41],{},[43,3945,46],{"stretchy":45},[39,3947,49],{},[43,3949,52],{"stretchy":45},[54,3951,1182],{"encoding":56},[20,3953,3955,3973],{"className":3954,"ariaHidden":62},[61],[20,3956,3958,3961,3964,3967,3970],{"className":3957},[66],[20,3959],{"className":3960,"style":1192},[70],[20,3962,1169],{"className":3963,"style":1196},[75,76],[20,3965],{"className":3966,"style":135},[134],[20,3968,320],{"className":3969},[139],[20,3971],{"className":3972,"style":135},[134],[20,3974,3976,3979,3982,3985,3988],{"className":3975},[66],[20,3977],{"className":3978,"style":71},[70],[20,3980,41],{"className":3981,"style":77},[75,76],[20,3983,46],{"className":3984},[81],[20,3986,49],{"className":3987},[75,76],[20,3989,52],{"className":3990},[88],[20,3992,3994,4011],{"className":3993},[23],[20,3995,3997],{"className":3996},[27],[29,3998,3999],{"xmlns":31},[33,4000,4001,4009],{},[36,4002,4003,4005,4007],{},[39,4004,49],{},[43,4006,320],{},[39,4008,104],{},[54,4010,3549],{"encoding":56},[20,4012,4014,4032],{"className":4013,"ariaHidden":62},[61],[20,4015,4017,4020,4023,4026,4029],{"className":4016},[66],[20,4018],{"className":4019,"style":665},[70],[20,4021,49],{"className":4022},[75,76],[20,4024],{"className":4025,"style":135},[134],[20,4027,320],{"className":4028},[139],[20,4030],{"className":4031,"style":135},[134],[20,4033,4035,4038],{"className":4034},[66],[20,4036],{"className":4037,"style":665},[70],[20,4039,104],{"className":4040},[75,76],"における微分係数",[20,4043,4045,4068],{"className":4044},[23],[20,4046,4048],{"className":4047},[27],[29,4049,4050],{"xmlns":31},[33,4051,4052,4066],{},[36,4053,4054,4060,4062,4064],{},[322,4055,4056,4058],{},[39,4057,41],{},[43,4059,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,4061,46],{"stretchy":45},[39,4063,104],{},[43,4065,52],{"stretchy":45},[54,4067,1309],{"encoding":56},[20,4069,4071],{"className":4070,"ariaHidden":62},[61],[20,4072,4074,4077,4109,4112,4115],{"className":4073},[66],[20,4075],{"className":4076,"style":1026},[70],[20,4078,4080,4083],{"className":4079},[75],[20,4081,41],{"className":4082,"style":77},[75,76],[20,4084,4086],{"className":4085},[550],[20,4087,4089],{"className":4088},[396],[20,4090,4092],{"className":4091},[401],[20,4093,4095],{"className":4094,"style":560},[405],[20,4096,4097,4100],{"style":563},[20,4098],{"className":4099,"style":567},[413],[20,4101,4103],{"className":4102},[448,449,450,451],[20,4104,4106],{"className":4105},[75,451],[20,4107,330],{"className":4108},[75,451],[20,4110,46],{"className":4111},[81],[20,4113,104],{"className":4114},[75,76],[20,4116,52],{"className":4117},[88],"は，",[20,4120,4122,4135],{"className":4121},[23],[20,4123,4125],{"className":4124},[27],[29,4126,4127],{"xmlns":31},[33,4128,4129,4133],{},[36,4130,4131],{},[39,4132,1530],{},[54,4134,1530],{"encoding":56},[20,4136,4138],{"className":4137,"ariaHidden":62},[61],[20,4139,4141,4144],{"className":4140},[66],[20,4142],{"className":4143,"style":167},[70],[20,4145,1530],{"className":4146},[75,76],"が限りなく",[20,4149,4151,4164],{"className":4150},[23],[20,4152,4154],{"className":4153},[27],[29,4155,4156],{"xmlns":31},[33,4157,4158,4162],{},[36,4159,4160],{},[1535,4161,283],{},[54,4163,283],{"encoding":56},[20,4165,4167],{"className":4166,"ariaHidden":62},[61],[20,4168,4170,4174],{"className":4169},[66],[20,4171],{"className":4172,"style":4173},[70],"height:0.6444em;",[20,4175,283],{"className":4176},[75],"に近づくことで，",[20,4179,4181,4204],{"className":4180},[23],[20,4182,4184],{"className":4183},[27],[29,4185,4186],{"xmlns":31},[33,4187,4188,4202],{},[36,4189,4190,4192,4194,4196,4198,4200],{},[39,4191,1169],{},[43,4193,320],{},[39,4195,41],{},[43,4197,46],{"stretchy":45},[39,4199,49],{},[43,4201,52],{"stretchy":45},[54,4203,1182],{"encoding":56},[20,4205,4207,4225],{"className":4206,"ariaHidden":62},[61],[20,4208,4210,4213,4216,4219,4222],{"className":4209},[66],[20,4211],{"className":4212,"style":1192},[70],[20,4214,1169],{"className":4215,"style":1196},[75,76],[20,4217],{"className":4218,"style":135},[134],[20,4220,320],{"className":4221},[139],[20,4223],{"className":4224,"style":135},[134],[20,4226,4228,4231,4234,4237,4240],{"className":4227},[66],[20,4229],{"className":4230,"style":71},[70],[20,4232,41],{"className":4233,"style":77},[75,76],[20,4235,46],{"className":4236},[81],[20,4238,49],{"className":4239},[75,76],[20,4241,52],{"className":4242},[88],"上の点",[20,4245,4247,4274],{"className":4246},[23],[20,4248,4250],{"className":4249},[27],[29,4251,4252],{"xmlns":31},[33,4253,4254,4272],{},[36,4255,4256,4258,4260,4262,4264,4266,4268,4270],{},[43,4257,46],{"stretchy":45},[39,4259,104],{},[43,4261,868],{"separator":62},[39,4263,41],{},[43,4265,46],{"stretchy":45},[39,4267,104],{},[43,4269,52],{"stretchy":45},[43,4271,52],{"stretchy":45},[54,4273,881],{"encoding":56},[20,4275,4277],{"className":4276,"ariaHidden":62},[61],[20,4278,4280,4283,4286,4289,4292,4295,4298,4301,4304],{"className":4279},[66],[20,4281],{"className":4282,"style":71},[70],[20,4284,46],{"className":4285},[81],[20,4287,104],{"className":4288},[75,76],[20,4290,868],{"className":4291},[900],[20,4293],{"className":4294,"style":904},[134],[20,4296,41],{"className":4297,"style":77},[75,76],[20,4299,46],{"className":4300},[81],[20,4302,104],{"className":4303},[75,76],[20,4305,917],{"className":4306},[88],"における接線の傾きを表すから，接線の方程式は",[20,4309,4311],{"className":4310},[251],[20,4312,4314,4362],{"className":4313},[23],[20,4315,4317],{"className":4316},[27],[29,4318,4319],{"xmlns":31,"display":260},[33,4320,4321,4359],{},[36,4322,4323,4325,4327,4329,4331,4333,4335,4337,4343,4345,4347,4349,4351,4353,4355,4357],{},[39,4324,1169],{},[43,4326,301],{},[39,4328,41],{},[43,4330,46],{"stretchy":45},[39,4332,104],{},[43,4334,52],{"stretchy":45},[43,4336,320],{},[322,4338,4339,4341],{},[39,4340,41],{},[43,4342,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,4344,46],{"stretchy":45},[39,4346,104],{},[43,4348,52],{"stretchy":45},[43,4350,46],{"stretchy":45},[39,4352,49],{},[43,4354,301],{},[39,4356,104],{},[43,4358,52],{"stretchy":45},[54,4360,4361],{"encoding":56},"y - f(a) = f'(a)(x-a)",[20,4363,4365,4384,4411,4473],{"className":4364,"ariaHidden":62},[61],[20,4366,4368,4372,4375,4378,4381],{"className":4367},[66],[20,4369],{"className":4370,"style":4371},[70],"height:0.7778em;vertical-align:-0.1944em;",[20,4373,1169],{"className":4374,"style":1196},[75,76],[20,4376],{"className":4377,"style":1759},[134],[20,4379,301],{"className":4380},[461],[20,4382],{"className":4383,"style":1759},[134],[20,4385,4387,4390,4393,4396,4399,4402,4405,4408],{"className":4386},[66],[20,4388],{"className":4389,"style":71},[70],[20,4391,41],{"className":4392,"style":77},[75,76],[20,4394,46],{"className":4395},[81],[20,4397,104],{"className":4398},[75,76],[20,4400,52],{"className":4401},[88],[20,4403],{"className":4404,"style":135},[134],[20,4406,320],{"className":4407},[139],[20,4409],{"className":4410,"style":135},[134],[20,4412,4414,4417,4449,4452,4455,4458,4461,4464,4467,4470],{"className":4413},[66],[20,4415],{"className":4416,"style":1578},[70],[20,4418,4420,4423],{"className":4419},[75],[20,4421,41],{"className":4422,"style":77},[75,76],[20,4424,4426],{"className":4425},[550],[20,4427,4429],{"className":4428},[396],[20,4430,4432],{"className":4431},[401],[20,4433,4435],{"className":4434,"style":1597},[405],[20,4436,4437,4440],{"style":1600},[20,4438],{"className":4439,"style":567},[413],[20,4441,4443],{"className":4442},[448,449,450,451],[20,4444,4446],{"className":4445},[75,451],[20,4447,330],{"className":4448},[75,451],[20,4450,46],{"className":4451},[81],[20,4453,104],{"className":4454},[75,76],[20,4456,52],{"className":4457},[88],[20,4459,46],{"className":4460},[81],[20,4462,49],{"className":4463},[75,76],[20,4465],{"className":4466,"style":1759},[134],[20,4468,301],{"className":4469},[461],[20,4471],{"className":4472,"style":1759},[134],[20,4474,4476,4479,4482],{"className":4475},[66],[20,4477],{"className":4478,"style":71},[70],[20,4480,104],{"className":4481},[75,76],[20,4483,52],{"className":4484},[88],[16,4486,4487,4488,4629],{},"また，",[20,4489,4491,4520],{"className":4490},[23],[20,4492,4494],{"className":4493},[27],[29,4495,4496],{"xmlns":31},[33,4497,4498,4517],{},[36,4499,4500,4506,4508,4510,4512,4515],{},[322,4501,4502,4504],{},[39,4503,41],{},[43,4505,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,4507,46],{"stretchy":45},[39,4509,104],{},[43,4511,52],{"stretchy":45},[43,4513,4514],{"mathvariant":328},"≠",[1535,4516,283],{},[54,4518,4519],{"encoding":56},"f'(a) \\neq 0",[20,4521,4523,4620],{"className":4522,"ariaHidden":62},[61],[20,4524,4526,4529,4561,4564,4567,4570,4573,4617],{"className":4525},[66],[20,4527],{"className":4528,"style":1026},[70],[20,4530,4532,4535],{"className":4531},[75],[20,4533,41],{"className":4534,"style":77},[75,76],[20,4536,4538],{"className":4537},[550],[20,4539,4541],{"className":4540},[396],[20,4542,4544],{"className":4543},[401],[20,4545,4547],{"className":4546,"style":560},[405],[20,4548,4549,4552],{"style":563},[20,4550],{"className":4551,"style":567},[413],[20,4553,4555],{"className":4554},[448,449,450,451],[20,4556,4558],{"className":4557},[75,451],[20,4559,330],{"className":4560},[75,451],[20,4562,46],{"className":4563},[81],[20,4565,104],{"className":4566},[75,76],[20,4568,52],{"className":4569},[88],[20,4571],{"className":4572,"style":135},[134],[20,4574,4576,4610,4614],{"className":4575},[139],[20,4577,4579],{"className":4578},[139],[20,4580,4583],{"className":4581},[75,4582],"vbox",[20,4584,4587],{"className":4585},[4586],"thinbox",[20,4588,4591,4595,4606],{"className":4589},[4590],"rlap",[20,4592],{"className":4593,"style":4594},[70],"height:0.8889em;vertical-align:-0.1944em;",[20,4596,4599],{"className":4597},[4598],"inner",[20,4600,4602],{"className":4601},[75],[20,4603,4605],{"className":4604},[139],"",[20,4607],{"className":4608},[4609],"fix",[20,4611],{"className":4612},[134,4613],"nobreak",[20,4615,320],{"className":4616},[139],[20,4618],{"className":4619,"style":135},[134],[20,4621,4623,4626],{"className":4622},[66],[20,4624],{"className":4625,"style":4173},[70],[20,4627,283],{"className":4628},[75],"の場合，法線の方程式は",[20,4631,4633],{"className":4632},[251],[20,4634,4636,4693],{"className":4635},[23],[20,4637,4639],{"className":4638},[27],[29,4640,4641],{"xmlns":31,"display":260},[33,4642,4643,4690],{},[36,4644,4645,4647,4649,4651,4653,4655,4657,4659,4661,4680,4682,4684,4686,4688],{},[39,4646,1169],{},[43,4648,301],{},[39,4650,41],{},[43,4652,46],{"stretchy":45},[39,4654,104],{},[43,4656,52],{"stretchy":45},[43,4658,320],{},[43,4660,301],{},[287,4662,4663,4666],{},[1535,4664,4665],{},"1",[36,4667,4668,4674,4676,4678],{},[322,4669,4670,4672],{},[39,4671,41],{},[43,4673,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,4675,46],{"stretchy":45},[39,4677,104],{},[43,4679,52],{"stretchy":45},[43,4681,46],{"stretchy":45},[39,4683,49],{},[43,4685,301],{},[39,4687,104],{},[43,4689,52],{"stretchy":45},[54,4691,4692],{"encoding":56},"y - f(a) = -\\frac{1}{f'(a)}(x-a)",[20,4694,4696,4714,4741,4870],{"className":4695,"ariaHidden":62},[61],[20,4697,4699,4702,4705,4708,4711],{"className":4698},[66],[20,4700],{"className":4701,"style":4371},[70],[20,4703,1169],{"className":4704,"style":1196},[75,76],[20,4706],{"className":4707,"style":1759},[134],[20,4709,301],{"className":4710},[461],[20,4712],{"className":4713,"style":1759},[134],[20,4715,4717,4720,4723,4726,4729,4732,4735,4738],{"className":4716},[66],[20,4718],{"className":4719,"style":71},[70],[20,4721,41],{"className":4722,"style":77},[75,76],[20,4724,46],{"className":4725},[81],[20,4727,104],{"className":4728},[75,76],[20,4730,52],{"className":4731},[88],[20,4733],{"className":4734,"style":135},[134],[20,4736,320],{"className":4737},[139],[20,4739],{"className":4740,"style":135},[134],[20,4742,4744,4748,4751,4855,4858,4861,4864,4867],{"className":4743},[66],[20,4745],{"className":4746,"style":4747},[70],"height:2.2574em;vertical-align:-0.936em;",[20,4749,301],{"className":4750},[75],[20,4752,4754,4757,4852],{"className":4753},[75],[20,4755],{"className":4756},[81,424],[20,4758,4760],{"className":4759},[287],[20,4761,4763,4843],{"className":4762},[396,397],[20,4764,4766,4840],{"className":4765},[401],[20,4767,4770,4821,4829],{"className":4768,"style":4769},[405],"height:1.3214em;",[20,4771,4772,4775],{"style":1720},[20,4773],{"className":4774,"style":444},[413],[20,4776,4778,4812,4815,4818],{"className":4777},[75],[20,4779,4781,4784],{"className":4780},[75],[20,4782,41],{"className":4783,"style":77},[75,76],[20,4785,4787],{"className":4786},[550],[20,4788,4790],{"className":4789},[396],[20,4791,4793],{"className":4792},[401],[20,4794,4797],{"className":4795,"style":4796},[405],"height:0.6779em;",[20,4798,4800,4803],{"style":4799},"top:-2.989em;margin-right:0.05em;",[20,4801],{"className":4802,"style":567},[413],[20,4804,4806],{"className":4805},[448,449,450,451],[20,4807,4809],{"className":4808},[75,451],[20,4810,330],{"className":4811},[75,451],[20,4813,46],{"className":4814},[81],[20,4816,104],{"className":4817},[75,76],[20,4819,52],{"className":4820},[88],[20,4822,4823,4826],{"style":467},[20,4824],{"className":4825,"style":444},[413],[20,4827],{"className":4828,"style":475},[474],[20,4830,4831,4834],{"style":1740},[20,4832],{"className":4833,"style":444},[413],[20,4835,4837],{"className":4836},[75],[20,4838,4665],{"className":4839},[75],[20,4841,519],{"className":4842},[518],[20,4844,4846],{"className":4845},[401],[20,4847,4850],{"className":4848,"style":4849},[405],"height:0.936em;",[20,4851],{},[20,4853],{"className":4854},[88,424],[20,4856,46],{"className":4857},[81],[20,4859,49],{"className":4860},[75,76],[20,4862],{"className":4863,"style":1759},[134],[20,4865,301],{"className":4866},[461],[20,4868],{"className":4869,"style":1759},[134],[20,4871,4873,4876,4879],{"className":4872},[66],[20,4874],{"className":4875,"style":71},[70],[20,4877,104],{"className":4878},[75,76],[20,4880,52],{"className":4881},[88],[4883,4884,4886],"h3",{"id":4885},"_2曲線が接する条件","2曲線が接する条件",[16,4888,4889,4917,4918,4949],{},[20,4890,4892,4905],{"className":4891},[23],[20,4893,4895],{"className":4894},[27],[29,4896,4897],{"xmlns":31},[33,4898,4899,4903],{},[36,4900,4901],{},[39,4902,49],{},[54,4904,49],{"encoding":56},[20,4906,4908],{"className":4907,"ariaHidden":62},[61],[20,4909,4911,4914],{"className":4910},[66],[20,4912],{"className":4913,"style":665},[70],[20,4915,49],{"className":4916},[75,76],"座標を",[20,4919,4921,4936],{"className":4920},[23],[20,4922,4924],{"className":4923},[27],[29,4925,4926],{"xmlns":31},[33,4927,4928,4933],{},[36,4929,4930],{},[39,4931,4932],{},"α",[54,4934,4935],{"encoding":56},"\\alpha",[20,4937,4939],{"className":4938,"ariaHidden":62},[61],[20,4940,4942,4945],{"className":4941},[66],[20,4943],{"className":4944,"style":665},[70],[20,4946,4932],{"className":4947,"style":4948},[75,76],"margin-right:0.0037em;","とする接点で，接線が一致すると考え，",[20,4951,4953],{"className":4952},[251],[20,4954,4956,5032],{"className":4955},[23],[20,4957,4959],{"className":4958},[27],[29,4960,4961],{"xmlns":31,"display":260},[33,4962,4963,5029],{},[36,4964,4965,4967],{},[43,4966,267],{"fence":62},[269,4968,4969,4995],{"rowspacing":271,"columnalign":272,"columnspacing":273},[275,4970,4971],{},[278,4972,4973],{},[281,4974,4975],{"scriptlevel":283,"displaystyle":45},[36,4976,4977,4979,4981,4983,4985,4987,4989,4991,4993],{},[39,4978,41],{},[43,4980,46],{"stretchy":45},[39,4982,104],{},[43,4984,52],{"stretchy":45},[43,4986,320],{},[39,4988,2526],{},[43,4990,46],{"stretchy":45},[39,4992,104],{},[43,4994,52],{"stretchy":45},[275,4996,4997],{},[278,4998,4999],{},[281,5000,5001],{"scriptlevel":283,"displaystyle":45},[36,5002,5003,5009,5011,5013,5015,5017,5023,5025,5027],{},[322,5004,5005,5007],{},[39,5006,41],{},[43,5008,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,5010,46],{"stretchy":45},[39,5012,104],{},[43,5014,52],{"stretchy":45},[43,5016,320],{},[322,5018,5019,5021],{},[39,5020,2526],{},[43,5022,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,5024,46],{"stretchy":45},[39,5026,104],{},[43,5028,52],{"stretchy":45},[54,5030,5031],{"encoding":56},"\\begin{cases}\n    f(a)=g(a) \\\\\n    f'(a)=g'(a)\n\\end{cases}",[20,5033,5035],{"className":5034,"ariaHidden":62},[61],[20,5036,5038,5041],{"className":5037},[66],[20,5039],{"className":5040,"style":368},[70],[20,5042,5044,5050,5224],{"className":5043},[372],[20,5045,5047],{"className":5046,"style":377},[81,376],[20,5048,267],{"className":5049},[381,382],[20,5051,5053],{"className":5052},[75],[20,5054,5056],{"className":5055},[269],[20,5057,5059],{"className":5058},[392],[20,5060,5062,5215],{"className":5061},[396,397],[20,5063,5065,5212],{"className":5064},[401],[20,5066,5069,5112],{"className":5067,"style":5068},[405],"height:1.69em;",[20,5070,5072,5076],{"style":5071},"top:-3.69em;",[20,5073],{"className":5074,"style":5075},[413],"height:3.008em;",[20,5077,5079,5082,5085,5088,5091,5094,5097,5100,5103,5106,5109],{"className":5078},[75],[20,5080,41],{"className":5081,"style":77},[75,76],[20,5083,46],{"className":5084},[81],[20,5086,104],{"className":5087},[75,76],[20,5089,52],{"className":5090},[88],[20,5092],{"className":5093,"style":135},[134],[20,5095,320],{"className":5096},[139],[20,5098],{"className":5099,"style":135},[134],[20,5101,2526],{"className":5102,"style":1196},[75,76],[20,5104,46],{"className":5105},[81],[20,5107,104],{"className":5108},[75,76],[20,5110,52],{"className":5111},[88],[20,5113,5115,5118],{"style":5114},"top:-2.25em;",[20,5116],{"className":5117,"style":5075},[413],[20,5119,5121,5153,5156,5159,5162,5165,5168,5171,5203,5206,5209],{"className":5120},[75],[20,5122,5124,5127],{"className":5123},[75],[20,5125,41],{"className":5126,"style":77},[75,76],[20,5128,5130],{"className":5129},[550],[20,5131,5133],{"className":5132},[396],[20,5134,5136],{"className":5135},[401],[20,5137,5139],{"className":5138,"style":560},[405],[20,5140,5141,5144],{"style":563},[20,5142],{"className":5143,"style":567},[413],[20,5145,5147],{"className":5146},[448,449,450,451],[20,5148,5150],{"className":5149},[75,451],[20,5151,330],{"className":5152},[75,451],[20,5154,46],{"className":5155},[81],[20,5157,104],{"className":5158},[75,76],[20,5160,52],{"className":5161},[88],[20,5163],{"className":5164,"style":135},[134],[20,5166,320],{"className":5167},[139],[20,5169],{"className":5170,"style":135},[134],[20,5172,5174,5177],{"className":5173},[75],[20,5175,2526],{"className":5176,"style":1196},[75,76],[20,5178,5180],{"className":5179},[550],[20,5181,5183],{"className":5182},[396],[20,5184,5186],{"className":5185},[401],[20,5187,5189],{"className":5188,"style":560},[405],[20,5190,5191,5194],{"style":563},[20,5192],{"className":5193,"style":567},[413],[20,5195,5197],{"className":5196},[448,449,450,451],[20,5198,5200],{"className":5199},[75,451],[20,5201,330],{"className":5202},[75,451],[20,5204,46],{"className":5205},[81],[20,5207,104],{"className":5208},[75,76],[20,5210,52],{"className":5211},[88],[20,5213,519],{"className":5214},[518],[20,5216,5218],{"className":5217},[401],[20,5219,5222],{"className":5220,"style":5221},[405],"height:1.19em;",[20,5223],{},[20,5225],{"className":5226},[88,424],{"title":1129,"searchDepth":1130,"depth":1130,"links":5228},[5229,5230,5231],{"id":2823,"depth":1130,"text":2824},{"id":2830,"depth":1130,"text":2831},{"id":3524,"depth":1130,"text":3525,"children":5232},[5233],{"id":4885,"depth":5234,"text":4886},3,{},"\u002Fdict\u002Fdifferential-coefficient",{"title":2818,"description":1129},"dict\u002Fdifferential-coefficient\u002Findex","ShNV2UXn1EvLqL7CbufsYv_1HOloqQbasxHHSVpcFas","\u002Fcontent\u002Fdifferential-coefficient",{"id":5242,"title":5243,"body":5244,"category":1134,"description":1129,"draft":1135,"extension":1136,"meta":10256,"navigation":1138,"path":10257,"seo":10258,"stem":10259,"__hash__":10260,"actualPath":10261},"dictionary\u002Fdict\u002Fdifferential-function\u002Findex.md","微分法",{"type":8,"value":5245,"toc":10244},[5246,5248,5427,5508,5576,5841,5845,5848,5996,6210,6213,6504,6990,7353,7357,7612,7899,8208,8577,8610,8840,8844],[11,5247,1152],{"id":1151},[16,5249,5250,2091,5278,2135,5321,2212,5397,2241,5425,2245],{},[20,5251,5253,5266],{"className":5252},[23],[20,5254,5256],{"className":5255},[27],[29,5257,5258],{"xmlns":31},[33,5259,5260,5264],{},[36,5261,5262],{},[39,5263,49],{},[54,5265,49],{"encoding":56},[20,5267,5269],{"className":5268,"ariaHidden":62},[61],[20,5270,5272,5275],{"className":5271},[66],[20,5273],{"className":5274,"style":665},[70],[20,5276,49],{"className":5277},[75,76],[20,5279,5281,5300],{"className":5280},[23],[20,5282,5284],{"className":5283},[27],[29,5285,5286],{"xmlns":31},[33,5287,5288,5298],{},[36,5289,5290,5292,5294,5296],{},[39,5291,41],{},[43,5293,46],{"stretchy":45},[39,5295,49],{},[43,5297,52],{"stretchy":45},[54,5299,57],{"encoding":56},[20,5301,5303],{"className":5302,"ariaHidden":62},[61],[20,5304,5306,5309,5312,5315,5318],{"className":5305},[66],[20,5307],{"className":5308,"style":71},[70],[20,5310,41],{"className":5311,"style":77},[75,76],[20,5313,46],{"className":5314},[81],[20,5316,49],{"className":5317},[75,76],[20,5319,52],{"className":5320},[88],[20,5322,5324,5347],{"className":5323},[23],[20,5325,5327],{"className":5326},[27],[29,5328,5329],{"xmlns":31},[33,5330,5331,5345],{},[36,5332,5333,5339,5341,5343],{},[322,5334,5335,5337],{},[39,5336,41],{},[43,5338,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,5340,46],{"stretchy":45},[39,5342,49],{},[43,5344,52],{"stretchy":45},[54,5346,1387],{"encoding":56},[20,5348,5350],{"className":5349,"ariaHidden":62},[61],[20,5351,5353,5356,5388,5391,5394],{"className":5352},[66],[20,5354],{"className":5355,"style":1026},[70],[20,5357,5359,5362],{"className":5358},[75],[20,5360,41],{"className":5361,"style":77},[75,76],[20,5363,5365],{"className":5364},[550],[20,5366,5368],{"className":5367},[396],[20,5369,5371],{"className":5370},[401],[20,5372,5374],{"className":5373,"style":560},[405],[20,5375,5376,5379],{"style":563},[20,5377],{"className":5378,"style":567},[413],[20,5380,5382],{"className":5381},[448,449,450,451],[20,5383,5385],{"className":5384},[75,451],[20,5386,330],{"className":5387},[75,451],[20,5389,46],{"className":5390},[81],[20,5392,49],{"className":5393},[75,76],[20,5395,52],{"className":5396},[88],[20,5398,5400,5413],{"className":5399},[23],[20,5401,5403],{"className":5402},[27],[29,5404,5405],{"xmlns":31},[33,5406,5407,5411],{},[36,5408,5409],{},[39,5410,49],{},[54,5412,49],{"encoding":56},[20,5414,5416],{"className":5415,"ariaHidden":62},[61],[20,5417,5419,5422],{"className":5418},[66],[20,5420],{"className":5421,"style":665},[70],[20,5423,49],{"className":5424},[75,76],[678,5426,2244],{},[11,5428,5430,5431,5507],{"id":5429},"_2-fxfxfxの符号と関数の増減","2. ",[20,5432,5434,5457],{"className":5433},[23],[20,5435,5437],{"className":5436},[27],[29,5438,5439],{"xmlns":31},[33,5440,5441,5455],{},[36,5442,5443,5449,5451,5453],{},[322,5444,5445,5447],{},[39,5446,41],{},[43,5448,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,5450,46],{"stretchy":45},[39,5452,49],{},[43,5454,52],{"stretchy":45},[54,5456,1387],{"encoding":56},[20,5458,5460],{"className":5459,"ariaHidden":62},[61],[20,5461,5463,5466,5498,5501,5504],{"className":5462},[66],[20,5464],{"className":5465,"style":1026},[70],[20,5467,5469,5472],{"className":5468},[75],[20,5470,41],{"className":5471,"style":77},[75,76],[20,5473,5475],{"className":5474},[550],[20,5476,5478],{"className":5477},[396],[20,5479,5481],{"className":5480},[401],[20,5482,5484],{"className":5483,"style":560},[405],[20,5485,5486,5489],{"style":563},[20,5487],{"className":5488,"style":567},[413],[20,5490,5492],{"className":5491},[448,449,450,451],[20,5493,5495],{"className":5494},[75,451],[20,5496,330],{"className":5497},[75,451],[20,5499,46],{"className":5500},[81],[20,5502,49],{"className":5503},[75,76],[20,5505,52],{"className":5506},[88],"の符号と関数の増減",[16,5509,18,5510,5575],{},[20,5511,5513,5536],{"className":5512},[23],[20,5514,5516],{"className":5515},[27],[29,5517,5518],{"xmlns":31},[33,5519,5520,5534],{},[36,5521,5522,5524,5526,5528,5530,5532],{},[39,5523,1169],{},[43,5525,320],{},[39,5527,41],{},[43,5529,46],{"stretchy":45},[39,5531,49],{},[43,5533,52],{"stretchy":45},[54,5535,1182],{"encoding":56},[20,5537,5539,5557],{"className":5538,"ariaHidden":62},[61],[20,5540,5542,5545,5548,5551,5554],{"className":5541},[66],[20,5543],{"className":5544,"style":1192},[70],[20,5546,1169],{"className":5547,"style":1196},[75,76],[20,5549],{"className":5550,"style":135},[134],[20,5552,320],{"className":5553},[139],[20,5555],{"className":5556,"style":135},[134],[20,5558,5560,5563,5566,5569,5572],{"className":5559},[66],[20,5561],{"className":5562,"style":71},[70],[20,5564,41],{"className":5565,"style":77},[75,76],[20,5567,46],{"className":5568},[81],[20,5570,49],{"className":5571},[75,76],[20,5573,52],{"className":5574},[88],"の値の増減は，",[5577,5578,5579,5710],"ul",{},[690,5580,5581,5680,5681,5709],{},[20,5582,5584,5612],{"className":5583},[23],[20,5585,5587],{"className":5586},[27],[29,5588,5589],{"xmlns":31},[33,5590,5591,5609],{},[36,5592,5593,5599,5601,5603,5605,5607],{},[322,5594,5595,5597],{},[39,5596,41],{},[43,5598,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,5600,46],{"stretchy":45},[39,5602,49],{},[43,5604,52],{"stretchy":45},[43,5606,188],{},[1535,5608,283],{},[54,5610,5611],{"encoding":56},"f'(x) \u003C 0",[20,5613,5615,5671],{"className":5614,"ariaHidden":62},[61],[20,5616,5618,5621,5653,5656,5659,5662,5665,5668],{"className":5617},[66],[20,5619],{"className":5620,"style":1026},[70],[20,5622,5624,5627],{"className":5623},[75],[20,5625,41],{"className":5626,"style":77},[75,76],[20,5628,5630],{"className":5629},[550],[20,5631,5633],{"className":5632},[396],[20,5634,5636],{"className":5635},[401],[20,5637,5639],{"className":5638,"style":560},[405],[20,5640,5641,5644],{"style":563},[20,5642],{"className":5643,"style":567},[413],[20,5645,5647],{"className":5646},[448,449,450,451],[20,5648,5650],{"className":5649},[75,451],[20,5651,330],{"className":5652},[75,451],[20,5654,46],{"className":5655},[81],[20,5657,49],{"className":5658},[75,76],[20,5660,52],{"className":5661},[88],[20,5663],{"className":5664,"style":135},[134],[20,5666,188],{"className":5667},[139],[20,5669],{"className":5670,"style":135},[134],[20,5672,5674,5677],{"className":5673},[66],[20,5675],{"className":5676,"style":4173},[70],[20,5678,283],{"className":5679},[75],"となる",[20,5682,5684,5697],{"className":5683},[23],[20,5685,5687],{"className":5686},[27],[29,5688,5689],{"xmlns":31},[33,5690,5691,5695],{},[36,5692,5693],{},[39,5694,49],{},[54,5696,49],{"encoding":56},[20,5698,5700],{"className":5699,"ariaHidden":62},[61],[20,5701,5703,5706],{"className":5702},[66],[20,5704],{"className":5705,"style":665},[70],[20,5707,49],{"className":5708},[75,76],"の範囲で減少し，",[690,5711,5712,5680,5812,5840],{},[20,5713,5715,5743],{"className":5714},[23],[20,5716,5718],{"className":5717},[27],[29,5719,5720],{"xmlns":31},[33,5721,5722,5740],{},[36,5723,5724,5726,5728,5734,5736,5738],{},[1535,5725,283],{},[43,5727,188],{},[322,5729,5730,5732],{},[39,5731,41],{},[43,5733,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,5735,46],{"stretchy":45},[39,5737,49],{},[43,5739,52],{"stretchy":45},[54,5741,5742],{"encoding":56},"0 \u003C f'(x)",[20,5744,5746,5765],{"className":5745,"ariaHidden":62},[61],[20,5747,5749,5753,5756,5759,5762],{"className":5748},[66],[20,5750],{"className":5751,"style":5752},[70],"height:0.6835em;vertical-align:-0.0391em;",[20,5754,283],{"className":5755},[75],[20,5757],{"className":5758,"style":135},[134],[20,5760,188],{"className":5761},[139],[20,5763],{"className":5764,"style":135},[134],[20,5766,5768,5771,5803,5806,5809],{"className":5767},[66],[20,5769],{"className":5770,"style":1026},[70],[20,5772,5774,5777],{"className":5773},[75],[20,5775,41],{"className":5776,"style":77},[75,76],[20,5778,5780],{"className":5779},[550],[20,5781,5783],{"className":5782},[396],[20,5784,5786],{"className":5785},[401],[20,5787,5789],{"className":5788,"style":560},[405],[20,5790,5791,5794],{"style":563},[20,5792],{"className":5793,"style":567},[413],[20,5795,5797],{"className":5796},[448,449,450,451],[20,5798,5800],{"className":5799},[75,451],[20,5801,330],{"className":5802},[75,451],[20,5804,46],{"className":5805},[81],[20,5807,49],{"className":5808},[75,76],[20,5810,52],{"className":5811},[88],[20,5813,5815,5828],{"className":5814},[23],[20,5816,5818],{"className":5817},[27],[29,5819,5820],{"xmlns":31},[33,5821,5822,5826],{},[36,5823,5824],{},[39,5825,49],{},[54,5827,49],{"encoding":56},[20,5829,5831],{"className":5830,"ariaHidden":62},[61],[20,5832,5834,5837],{"className":5833},[66],[20,5835],{"className":5836,"style":665},[70],[20,5838,49],{"className":5839},[75,76],"の範囲で増加する．",[11,5842,5844],{"id":5843},"_3-公式","3. 公式",[4883,5846,5847],{"id":5847},"基本的な関数の微分",[20,5849,5851],{"className":5850},[251],[20,5852,5854,5895],{"className":5853},[23],[20,5855,5857],{"className":5856},[27],[29,5858,5859],{"xmlns":31,"display":260},[33,5860,5861,5892],{},[36,5862,5863,5865,5867,5873,5875,5877,5879,5881,5885,5887,5890],{},[43,5864,46],{"stretchy":45},[39,5866,335],{},[322,5868,5869,5871],{},[43,5870,52],{"stretchy":45},[43,5872,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,5874,320],{},[1535,5876,283],{},[134,5878],{"width":273},[43,5880,46],{"stretchy":45},[5882,5883,5884],"mtext",{},"ただし ",[39,5886,335],{},[5882,5888,5889],{}," は定数",[43,5891,52],{"stretchy":45},[54,5893,5894],{"encoding":56},"(c)' = 0 \\quad (\\text{ただし } c \\text{ は定数})",[20,5896,5898,5951],{"className":5897,"ariaHidden":62},[61],[20,5899,5901,5904,5907,5910,5942,5945,5948],{"className":5900},[66],[20,5902],{"className":5903,"style":1578},[70],[20,5905,46],{"className":5906},[81],[20,5908,335],{"className":5909},[75,76],[20,5911,5913,5916],{"className":5912},[88],[20,5914,52],{"className":5915},[88],[20,5917,5919],{"className":5918},[550],[20,5920,5922],{"className":5921},[396],[20,5923,5925],{"className":5924},[401],[20,5926,5928],{"className":5927,"style":1597},[405],[20,5929,5930,5933],{"style":1600},[20,5931],{"className":5932,"style":567},[413],[20,5934,5936],{"className":5935},[448,449,450,451],[20,5937,5939],{"className":5938},[75,451],[20,5940,330],{"className":5941},[75,451],[20,5943],{"className":5944,"style":135},[134],[20,5946,320],{"className":5947},[139],[20,5949],{"className":5950,"style":135},[134],[20,5952,5954,5957,5960,5964,5967,5980,5983,5993],{"className":5953},[66],[20,5955],{"className":5956,"style":71},[70],[20,5958,283],{"className":5959},[75],[20,5961],{"className":5962,"style":5963},[134],"margin-right:1em;",[20,5965,46],{"className":5966},[81],[20,5968,5971,5976],{"className":5969},[75,5970],"text",[20,5972,5975],{"className":5973},[75,5974],"cjk_fallback","ただし",[20,5977,5979],{"className":5978},[75]," ",[20,5981,335],{"className":5982},[75,76],[20,5984,5986,5989],{"className":5985},[75,5970],[20,5987,5979],{"className":5988},[75],[20,5990,5992],{"className":5991},[75,5974],"は定数",[20,5994,52],{"className":5995},[88],[20,5997,5999],{"className":5998},[251],[20,6000,6002,6056],{"className":6001},[23],[20,6003,6005],{"className":6004},[27],[29,6006,6007],{"xmlns":31,"display":260},[33,6008,6009,6053],{},[36,6010,6011,6013,6020,6026,6028,6030,6042,6044,6046,6049,6051],{},[43,6012,46],{"stretchy":45},[322,6014,6015,6017],{},[39,6016,49],{},[39,6018,6019],{},"n",[322,6021,6022,6024],{},[43,6023,52],{"stretchy":45},[43,6025,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,6027,320],{},[39,6029,6019],{},[322,6031,6032,6034],{},[39,6033,49],{},[36,6035,6036,6038,6040],{},[39,6037,6019],{},[43,6039,301],{},[1535,6041,4665],{},[134,6043],{"width":273},[43,6045,46],{"stretchy":45},[5882,6047,6048],{},"実数 ",[39,6050,6019],{},[43,6052,52],{"stretchy":45},[54,6054,6055],{"encoding":56},"(x^n)' = n x^{n-1} \\quad (\\text{実数 } n)",[20,6057,6059,6139],{"className":6058,"ariaHidden":62},[61],[20,6060,6062,6065,6068,6098,6130,6133,6136],{"className":6061},[66],[20,6063],{"className":6064,"style":1578},[70],[20,6066,46],{"className":6067},[81],[20,6069,6071,6074],{"className":6070},[75],[20,6072,49],{"className":6073},[75,76],[20,6075,6077],{"className":6076},[550],[20,6078,6080],{"className":6079},[396],[20,6081,6083],{"className":6082},[401],[20,6084,6087],{"className":6085,"style":6086},[405],"height:0.7144em;",[20,6088,6089,6092],{"style":1600},[20,6090],{"className":6091,"style":567},[413],[20,6093,6095],{"className":6094},[448,449,450,451],[20,6096,6019],{"className":6097},[75,76,451],[20,6099,6101,6104],{"className":6100},[88],[20,6102,52],{"className":6103},[88],[20,6105,6107],{"className":6106},[550],[20,6108,6110],{"className":6109},[396],[20,6111,6113],{"className":6112},[401],[20,6114,6116],{"className":6115,"style":1597},[405],[20,6117,6118,6121],{"style":1600},[20,6119],{"className":6120,"style":567},[413],[20,6122,6124],{"className":6123},[448,449,450,451],[20,6125,6127],{"className":6126},[75,451],[20,6128,330],{"className":6129},[75,451],[20,6131],{"className":6132,"style":135},[134],[20,6134,320],{"className":6135},[139],[20,6137],{"className":6138,"style":135},[134],[20,6140,6142,6146,6149,6188,6191,6194,6204,6207],{"className":6141},[66],[20,6143],{"className":6144,"style":6145},[70],"height:1.1141em;vertical-align:-0.25em;",[20,6147,6019],{"className":6148},[75,76],[20,6150,6152,6155],{"className":6151},[75],[20,6153,49],{"className":6154},[75,76],[20,6156,6158],{"className":6157},[550],[20,6159,6161],{"className":6160},[396],[20,6162,6164],{"className":6163},[401],[20,6165,6168],{"className":6166,"style":6167},[405],"height:0.8641em;",[20,6169,6170,6173],{"style":1600},[20,6171],{"className":6172,"style":567},[413],[20,6174,6176],{"className":6175},[448,449,450,451],[20,6177,6179,6182,6185],{"className":6178},[75,451],[20,6180,6019],{"className":6181},[75,76,451],[20,6183,301],{"className":6184},[461,451],[20,6186,4665],{"className":6187},[75,451],[20,6189],{"className":6190,"style":5963},[134],[20,6192,46],{"className":6193},[81],[20,6195,6197,6201],{"className":6196},[75,5970],[20,6198,6200],{"className":6199},[75,5974],"実数",[20,6202,5979],{"className":6203},[75],[20,6205,6019],{"className":6206},[75,76],[20,6208,52],{"className":6209},[88],[4883,6211,6212],{"id":6212},"積と商の微分公式",[20,6214,6216],{"className":6215},[251],[20,6217,6219,6300],{"className":6218},[23],[20,6220,6222],{"className":6221},[27],[29,6223,6224],{"xmlns":31,"display":260},[33,6225,6226,6297],{},[36,6227,6228,6230,6232,6234,6236,6238,6240,6242,6244,6246,6253,6255,6261,6263,6265,6267,6269,6271,6273,6275,6277,6279,6281,6283,6285,6291,6293,6295],{},[43,6229,267],{"stretchy":45},[39,6231,41],{},[43,6233,46],{"stretchy":45},[39,6235,49],{},[43,6237,52],{"stretchy":45},[39,6239,2526],{},[43,6241,46],{"stretchy":45},[39,6243,49],{},[43,6245,52],{"stretchy":45},[322,6247,6248,6251],{},[43,6249,6250],{"stretchy":45},"}",[43,6252,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,6254,320],{},[322,6256,6257,6259],{},[39,6258,41],{},[43,6260,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,6262,46],{"stretchy":45},[39,6264,49],{},[43,6266,52],{"stretchy":45},[39,6268,2526],{},[43,6270,46],{"stretchy":45},[39,6272,49],{},[43,6274,52],{"stretchy":45},[43,6276,1549],{},[39,6278,41],{},[43,6280,46],{"stretchy":45},[39,6282,49],{},[43,6284,52],{"stretchy":45},[322,6286,6287,6289],{},[39,6288,2526],{},[43,6290,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,6292,46],{"stretchy":45},[39,6294,49],{},[43,6296,52],{"stretchy":45},[54,6298,6299],{"encoding":56},"\\{f(x)g(x)\\}' = f'(x)g(x) + f(x)g'(x)",[20,6301,6303,6377,6445],{"className":6302,"ariaHidden":62},[61],[20,6304,6306,6309,6312,6315,6318,6321,6324,6327,6330,6333,6336,6368,6371,6374],{"className":6305},[66],[20,6307],{"className":6308,"style":1578},[70],[20,6310,267],{"className":6311},[81],[20,6313,41],{"className":6314,"style":77},[75,76],[20,6316,46],{"className":6317},[81],[20,6319,49],{"className":6320},[75,76],[20,6322,52],{"className":6323},[88],[20,6325,2526],{"className":6326,"style":1196},[75,76],[20,6328,46],{"className":6329},[81],[20,6331,49],{"className":6332},[75,76],[20,6334,52],{"className":6335},[88],[20,6337,6339,6342],{"className":6338},[88],[20,6340,6250],{"className":6341},[88],[20,6343,6345],{"className":6344},[550],[20,6346,6348],{"className":6347},[396],[20,6349,6351],{"className":6350},[401],[20,6352,6354],{"className":6353,"style":1597},[405],[20,6355,6356,6359],{"style":1600},[20,6357],{"className":6358,"style":567},[413],[20,6360,6362],{"className":6361},[448,449,450,451],[20,6363,6365],{"className":6364},[75,451],[20,6366,330],{"className":6367},[75,451],[20,6369],{"className":6370,"style":135},[134],[20,6372,320],{"className":6373},[139],[20,6375],{"className":6376,"style":135},[134],[20,6378,6380,6383,6415,6418,6421,6424,6427,6430,6433,6436,6439,6442],{"className":6379},[66],[20,6381],{"className":6382,"style":1578},[70],[20,6384,6386,6389],{"className":6385},[75],[20,6387,41],{"className":6388,"style":77},[75,76],[20,6390,6392],{"className":6391},[550],[20,6393,6395],{"className":6394},[396],[20,6396,6398],{"className":6397},[401],[20,6399,6401],{"className":6400,"style":1597},[405],[20,6402,6403,6406],{"style":1600},[20,6404],{"className":6405,"style":567},[413],[20,6407,6409],{"className":6408},[448,449,450,451],[20,6410,6412],{"className":6411},[75,451],[20,6413,330],{"className":6414},[75,451],[20,6416,46],{"className":6417},[81],[20,6419,49],{"className":6420},[75,76],[20,6422,52],{"className":6423},[88],[20,6425,2526],{"className":6426,"style":1196},[75,76],[20,6428,46],{"className":6429},[81],[20,6431,49],{"className":6432},[75,76],[20,6434,52],{"className":6435},[88],[20,6437],{"className":6438,"style":1759},[134],[20,6440,1549],{"className":6441},[461],[20,6443],{"className":6444,"style":1759},[134],[20,6446,6448,6451,6454,6457,6460,6463,6495,6498,6501],{"className":6447},[66],[20,6449],{"className":6450,"style":1578},[70],[20,6452,41],{"className":6453,"style":77},[75,76],[20,6455,46],{"className":6456},[81],[20,6458,49],{"className":6459},[75,76],[20,6461,52],{"className":6462},[88],[20,6464,6466,6469],{"className":6465},[75],[20,6467,2526],{"className":6468,"style":1196},[75,76],[20,6470,6472],{"className":6471},[550],[20,6473,6475],{"className":6474},[396],[20,6476,6478],{"className":6477},[401],[20,6479,6481],{"className":6480,"style":1597},[405],[20,6482,6483,6486],{"style":1600},[20,6484],{"className":6485,"style":567},[413],[20,6487,6489],{"className":6488},[448,449,450,451],[20,6490,6492],{"className":6491},[75,451],[20,6493,330],{"className":6494},[75,451],[20,6496,46],{"className":6497},[81],[20,6499,49],{"className":6500},[75,76],[20,6502,52],{"className":6503},[88],[20,6505,6507],{"className":6506},[251],[20,6508,6510,6621],{"className":6509},[23],[20,6511,6513],{"className":6512},[27],[29,6514,6515],{"xmlns":31,"display":260},[33,6516,6517,6618],{},[36,6518,6519,6551,6553],{},[322,6520,6521,6549],{},[36,6522,6523,6525,6547],{},[43,6524,267],{"fence":62},[287,6526,6527,6537],{},[36,6528,6529,6531,6533,6535],{},[39,6530,41],{},[43,6532,46],{"stretchy":45},[39,6534,49],{},[43,6536,52],{"stretchy":45},[36,6538,6539,6541,6543,6545],{},[39,6540,2526],{},[43,6542,46],{"stretchy":45},[39,6544,49],{},[43,6546,52],{"stretchy":45},[43,6548,6250],{"fence":62},[43,6550,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,6552,320],{},[287,6554,6555,6599],{},[36,6556,6557,6563,6565,6567,6569,6571,6573,6575,6577,6579,6581,6583,6585,6587,6593,6595,6597],{},[322,6558,6559,6561],{},[39,6560,41],{},[43,6562,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,6564,46],{"stretchy":45},[39,6566,49],{},[43,6568,52],{"stretchy":45},[39,6570,2526],{},[43,6572,46],{"stretchy":45},[39,6574,49],{},[43,6576,52],{"stretchy":45},[43,6578,301],{},[39,6580,41],{},[43,6582,46],{"stretchy":45},[39,6584,49],{},[43,6586,52],{"stretchy":45},[322,6588,6589,6591],{},[39,6590,2526],{},[43,6592,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,6594,46],{"stretchy":45},[39,6596,49],{},[43,6598,52],{"stretchy":45},[36,6600,6601,6603,6605,6607,6609,6611],{},[43,6602,267],{"stretchy":45},[39,6604,2526],{},[43,6606,46],{"stretchy":45},[39,6608,49],{},[43,6610,52],{"stretchy":45},[322,6612,6613,6615],{},[43,6614,6250],{"stretchy":45},[1535,6616,6617],{},"2",[54,6619,6620],{"encoding":56},"\\left\\{\\frac{f(x)}{g(x)}\\right\\}' = \\frac{f'(x)g(x) - f(x)g'(x)}{\\{g(x)\\}^2}",[20,6622,6624,6766],{"className":6623,"ariaHidden":62},[61],[20,6625,6627,6631,6757,6760,6763],{"className":6626},[66],[20,6628],{"className":6629,"style":6630},[70],"height:2.5418em;vertical-align:-0.95em;",[20,6632,6634,6729],{"className":6633},[372],[20,6635,6637,6643,6723],{"className":6636},[372],[20,6638,6640],{"className":6639,"style":377},[81,376],[20,6641,267],{"className":6642},[381,450],[20,6644,6646,6649,6720],{"className":6645},[75],[20,6647],{"className":6648},[81,424],[20,6650,6652],{"className":6651},[287],[20,6653,6655,6712],{"className":6654},[396,397],[20,6656,6658,6709],{"className":6657},[401],[20,6659,6661,6681,6689],{"className":6660,"style":1717},[405],[20,6662,6663,6666],{"style":1720},[20,6664],{"className":6665,"style":444},[413],[20,6667,6669,6672,6675,6678],{"className":6668},[75],[20,6670,2526],{"className":6671,"style":1196},[75,76],[20,6673,46],{"className":6674},[81],[20,6676,49],{"className":6677},[75,76],[20,6679,52],{"className":6680},[88],[20,6682,6683,6686],{"style":467},[20,6684],{"className":6685,"style":444},[413],[20,6687],{"className":6688,"style":475},[474],[20,6690,6691,6694],{"style":1740},[20,6692],{"className":6693,"style":444},[413],[20,6695,6697,6700,6703,6706],{"className":6696},[75],[20,6698,41],{"className":6699,"style":77},[75,76],[20,6701,46],{"className":6702},[81],[20,6704,49],{"className":6705},[75,76],[20,6707,52],{"className":6708},[88],[20,6710,519],{"className":6711},[518],[20,6713,6715],{"className":6714},[401],[20,6716,6718],{"className":6717,"style":4849},[405],[20,6719],{},[20,6721],{"className":6722},[88,424],[20,6724,6726],{"className":6725,"style":377},[88,376],[20,6727,6250],{"className":6728},[381,450],[20,6730,6732],{"className":6731},[550],[20,6733,6735],{"className":6734},[396],[20,6736,6738],{"className":6737},[401],[20,6739,6742],{"className":6740,"style":6741},[405],"height:1.5918em;",[20,6743,6745,6748],{"style":6744},"top:-3.9029em;margin-right:0.05em;",[20,6746],{"className":6747,"style":567},[413],[20,6749,6751],{"className":6750},[448,449,450,451],[20,6752,6754],{"className":6753},[75,451],[20,6755,330],{"className":6756},[75,451],[20,6758],{"className":6759,"style":135},[134],[20,6761,320],{"className":6762},[139],[20,6764],{"className":6765,"style":135},[134],[20,6767,6769,6773],{"className":6768},[66],[20,6770],{"className":6771,"style":6772},[70],"height:2.3649em;vertical-align:-0.936em;",[20,6774,6776,6779,6987],{"className":6775},[75],[20,6777],{"className":6778},[81,424],[20,6780,6782],{"className":6781},[287],[20,6783,6785,6979],{"className":6784},[396,397],[20,6786,6788,6976],{"className":6787},[401],[20,6789,6792,6845,6853],{"className":6790,"style":6791},[405],"height:1.4289em;",[20,6793,6794,6797],{"style":1720},[20,6795],{"className":6796,"style":444},[413],[20,6798,6800,6803,6806,6809,6812,6815],{"className":6799},[75],[20,6801,267],{"className":6802},[81],[20,6804,2526],{"className":6805,"style":1196},[75,76],[20,6807,46],{"className":6808},[81],[20,6810,49],{"className":6811},[75,76],[20,6813,52],{"className":6814},[88],[20,6816,6818,6821],{"className":6817},[88],[20,6819,6250],{"className":6820},[88],[20,6822,6824],{"className":6823},[550],[20,6825,6827],{"className":6826},[396],[20,6828,6830],{"className":6829},[401],[20,6831,6834],{"className":6832,"style":6833},[405],"height:0.7401em;",[20,6835,6836,6839],{"style":4799},[20,6837],{"className":6838,"style":567},[413],[20,6840,6842],{"className":6841},[448,449,450,451],[20,6843,6617],{"className":6844},[75,451],[20,6846,6847,6850],{"style":467},[20,6848],{"className":6849,"style":444},[413],[20,6851],{"className":6852,"style":475},[474],[20,6854,6855,6858],{"style":1740},[20,6856],{"className":6857,"style":444},[413],[20,6859,6861,6893,6896,6899,6902,6905,6908,6911,6914,6917,6920,6923,6926,6929,6932,6935,6967,6970,6973],{"className":6860},[75],[20,6862,6864,6867],{"className":6863},[75],[20,6865,41],{"className":6866,"style":77},[75,76],[20,6868,6870],{"className":6869},[550],[20,6871,6873],{"className":6872},[396],[20,6874,6876],{"className":6875},[401],[20,6877,6879],{"className":6878,"style":560},[405],[20,6880,6881,6884],{"style":563},[20,6882],{"className":6883,"style":567},[413],[20,6885,6887],{"className":6886},[448,449,450,451],[20,6888,6890],{"className":6889},[75,451],[20,6891,330],{"className":6892},[75,451],[20,6894,46],{"className":6895},[81],[20,6897,49],{"className":6898},[75,76],[20,6900,52],{"className":6901},[88],[20,6903,2526],{"className":6904,"style":1196},[75,76],[20,6906,46],{"className":6907},[81],[20,6909,49],{"className":6910},[75,76],[20,6912,52],{"className":6913},[88],[20,6915],{"className":6916,"style":1759},[134],[20,6918,301],{"className":6919},[461],[20,6921],{"className":6922,"style":1759},[134],[20,6924,41],{"className":6925,"style":77},[75,76],[20,6927,46],{"className":6928},[81],[20,6930,49],{"className":6931},[75,76],[20,6933,52],{"className":6934},[88],[20,6936,6938,6941],{"className":6937},[75],[20,6939,2526],{"className":6940,"style":1196},[75,76],[20,6942,6944],{"className":6943},[550],[20,6945,6947],{"className":6946},[396],[20,6948,6950],{"className":6949},[401],[20,6951,6953],{"className":6952,"style":560},[405],[20,6954,6955,6958],{"style":563},[20,6956],{"className":6957,"style":567},[413],[20,6959,6961],{"className":6960},[448,449,450,451],[20,6962,6964],{"className":6963},[75,451],[20,6965,330],{"className":6966},[75,451],[20,6968,46],{"className":6969},[81],[20,6971,49],{"className":6972},[75,76],[20,6974,52],{"className":6975},[88],[20,6977,519],{"className":6978},[518],[20,6980,6982],{"className":6981},[401],[20,6983,6985],{"className":6984,"style":4849},[405],[20,6986],{},[20,6988],{"className":6989},[88,424],[20,6991,6993],{"className":6992},[251],[20,6994,6996,7070],{"className":6995},[23],[20,6997,6999],{"className":6998},[27],[29,7000,7001],{"xmlns":31,"display":260},[33,7002,7003,7067],{},[36,7004,7005,7029,7031,7033],{},[322,7006,7007,7027],{},[36,7008,7009,7011,7025],{},[43,7010,267],{"fence":62},[287,7012,7013,7015],{},[1535,7014,4665],{},[36,7016,7017,7019,7021,7023],{},[39,7018,2526],{},[43,7020,46],{"stretchy":45},[39,7022,49],{},[43,7024,52],{"stretchy":45},[43,7026,6250],{"fence":62},[43,7028,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,7030,320],{},[43,7032,301],{},[287,7034,7035,7049],{},[36,7036,7037,7043,7045,7047],{},[322,7038,7039,7041],{},[39,7040,2526],{},[43,7042,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,7044,46],{"stretchy":45},[39,7046,49],{},[43,7048,52],{"stretchy":45},[36,7050,7051,7053,7055,7057,7059,7061],{},[43,7052,267],{"stretchy":45},[39,7054,2526],{},[43,7056,46],{"stretchy":45},[39,7058,49],{},[43,7060,52],{"stretchy":45},[322,7062,7063,7065],{},[43,7064,6250],{"stretchy":45},[1535,7066,6617],{},[54,7068,7069],{"encoding":56},"\\left\\{\\frac{1}{g(x)}\\right\\}' = -\\frac{g'(x)}{\\{g(x)\\}^2}",[20,7071,7073,7203],{"className":7072,"ariaHidden":62},[61],[20,7074,7076,7079,7194,7197,7200],{"className":7075},[66],[20,7077],{"className":7078,"style":6630},[70],[20,7080,7082,7168],{"className":7081},[372],[20,7083,7085,7091,7162],{"className":7084},[372],[20,7086,7088],{"className":7087,"style":377},[81,376],[20,7089,267],{"className":7090},[381,450],[20,7092,7094,7097,7159],{"className":7093},[75],[20,7095],{"className":7096},[81,424],[20,7098,7100],{"className":7099},[287],[20,7101,7103,7151],{"className":7102},[396,397],[20,7104,7106,7148],{"className":7105},[401],[20,7107,7109,7129,7137],{"className":7108,"style":4769},[405],[20,7110,7111,7114],{"style":1720},[20,7112],{"className":7113,"style":444},[413],[20,7115,7117,7120,7123,7126],{"className":7116},[75],[20,7118,2526],{"className":7119,"style":1196},[75,76],[20,7121,46],{"className":7122},[81],[20,7124,49],{"className":7125},[75,76],[20,7127,52],{"className":7128},[88],[20,7130,7131,7134],{"style":467},[20,7132],{"className":7133,"style":444},[413],[20,7135],{"className":7136,"style":475},[474],[20,7138,7139,7142],{"style":1740},[20,7140],{"className":7141,"style":444},[413],[20,7143,7145],{"className":7144},[75],[20,7146,4665],{"className":7147},[75],[20,7149,519],{"className":7150},[518],[20,7152,7154],{"className":7153},[401],[20,7155,7157],{"className":7156,"style":4849},[405],[20,7158],{},[20,7160],{"className":7161},[88,424],[20,7163,7165],{"className":7164,"style":377},[88,376],[20,7166,6250],{"className":7167},[381,450],[20,7169,7171],{"className":7170},[550],[20,7172,7174],{"className":7173},[396],[20,7175,7177],{"className":7176},[401],[20,7178,7180],{"className":7179,"style":6741},[405],[20,7181,7182,7185],{"style":6744},[20,7183],{"className":7184,"style":567},[413],[20,7186,7188],{"className":7187},[448,449,450,451],[20,7189,7191],{"className":7190},[75,451],[20,7192,330],{"className":7193},[75,451],[20,7195],{"className":7196,"style":135},[134],[20,7198,320],{"className":7199},[139],[20,7201],{"className":7202,"style":135},[134],[20,7204,7206,7209,7212],{"className":7205},[66],[20,7207],{"className":7208,"style":6772},[70],[20,7210,301],{"className":7211},[75],[20,7213,7215,7218,7350],{"className":7214},[75],[20,7216],{"className":7217},[81,424],[20,7219,7221],{"className":7220},[287],[20,7222,7224,7342],{"className":7223},[396,397],[20,7225,7227,7339],{"className":7226},[401],[20,7228,7230,7282,7290],{"className":7229,"style":6791},[405],[20,7231,7232,7235],{"style":1720},[20,7233],{"className":7234,"style":444},[413],[20,7236,7238,7241,7244,7247,7250,7253],{"className":7237},[75],[20,7239,267],{"className":7240},[81],[20,7242,2526],{"className":7243,"style":1196},[75,76],[20,7245,46],{"className":7246},[81],[20,7248,49],{"className":7249},[75,76],[20,7251,52],{"className":7252},[88],[20,7254,7256,7259],{"className":7255},[88],[20,7257,6250],{"className":7258},[88],[20,7260,7262],{"className":7261},[550],[20,7263,7265],{"className":7264},[396],[20,7266,7268],{"className":7267},[401],[20,7269,7271],{"className":7270,"style":6833},[405],[20,7272,7273,7276],{"style":4799},[20,7274],{"className":7275,"style":567},[413],[20,7277,7279],{"className":7278},[448,449,450,451],[20,7280,6617],{"className":7281},[75,451],[20,7283,7284,7287],{"style":467},[20,7285],{"className":7286,"style":444},[413],[20,7288],{"className":7289,"style":475},[474],[20,7291,7292,7295],{"style":1740},[20,7293],{"className":7294,"style":444},[413],[20,7296,7298,7330,7333,7336],{"className":7297},[75],[20,7299,7301,7304],{"className":7300},[75],[20,7302,2526],{"className":7303,"style":1196},[75,76],[20,7305,7307],{"className":7306},[550],[20,7308,7310],{"className":7309},[396],[20,7311,7313],{"className":7312},[401],[20,7314,7316],{"className":7315,"style":560},[405],[20,7317,7318,7321],{"style":563},[20,7319],{"className":7320,"style":567},[413],[20,7322,7324],{"className":7323},[448,449,450,451],[20,7325,7327],{"className":7326},[75,451],[20,7328,330],{"className":7329},[75,451],[20,7331,46],{"className":7332},[81],[20,7334,49],{"className":7335},[75,76],[20,7337,52],{"className":7338},[88],[20,7340,519],{"className":7341},[518],[20,7343,7345],{"className":7344},[401],[20,7346,7348],{"className":7347,"style":4849},[405],[20,7349],{},[20,7351],{"className":7352},[88,424],[4883,7354,7356],{"id":7355},"合成関数逆関数の微分公式","合成関数・逆関数の微分公式",[20,7358,7360],{"className":7359},[251],[20,7361,7363,7432],{"className":7362},[23],[20,7364,7366],{"className":7365},[27],[29,7367,7368],{"xmlns":31,"display":260},[33,7369,7370,7429],{},[36,7371,7372,7374,7376,7378,7380,7382,7384,7386,7388,7394,7396,7402,7404,7406,7408,7410,7412,7414,7417,7423,7425,7427],{},[43,7373,267],{"stretchy":45},[39,7375,41],{},[43,7377,46],{"stretchy":45},[39,7379,2526],{},[43,7381,46],{"stretchy":45},[39,7383,49],{},[43,7385,52],{"stretchy":45},[43,7387,52],{"stretchy":45},[322,7389,7390,7392],{},[43,7391,6250],{"stretchy":45},[43,7393,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,7395,320],{},[322,7397,7398,7400],{},[39,7399,41],{},[43,7401,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,7403,46],{"stretchy":45},[39,7405,2526],{},[43,7407,46],{"stretchy":45},[39,7409,49],{},[43,7411,52],{"stretchy":45},[43,7413,52],{"stretchy":45},[43,7415,7416],{},"⋅",[322,7418,7419,7421],{},[39,7420,2526],{},[43,7422,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,7424,46],{"stretchy":45},[39,7426,49],{},[43,7428,52],{"stretchy":45},[54,7430,7431],{"encoding":56},"\\{f(g(x))\\}' = f'(g(x)) \\cdot g'(x)",[20,7433,7435,7503,7565],{"className":7434,"ariaHidden":62},[61],[20,7436,7438,7441,7444,7447,7450,7453,7456,7459,7462,7494,7497,7500],{"className":7437},[66],[20,7439],{"className":7440,"style":1578},[70],[20,7442,267],{"className":7443},[81],[20,7445,41],{"className":7446,"style":77},[75,76],[20,7448,46],{"className":7449},[81],[20,7451,2526],{"className":7452,"style":1196},[75,76],[20,7454,46],{"className":7455},[81],[20,7457,49],{"className":7458},[75,76],[20,7460,917],{"className":7461},[88],[20,7463,7465,7468],{"className":7464},[88],[20,7466,6250],{"className":7467},[88],[20,7469,7471],{"className":7470},[550],[20,7472,7474],{"className":7473},[396],[20,7475,7477],{"className":7476},[401],[20,7478,7480],{"className":7479,"style":1597},[405],[20,7481,7482,7485],{"style":1600},[20,7483],{"className":7484,"style":567},[413],[20,7486,7488],{"className":7487},[448,449,450,451],[20,7489,7491],{"className":7490},[75,451],[20,7492,330],{"className":7493},[75,451],[20,7495],{"className":7496,"style":135},[134],[20,7498,320],{"className":7499},[139],[20,7501],{"className":7502,"style":135},[134],[20,7504,7506,7509,7541,7544,7547,7550,7553,7556,7559,7562],{"className":7505},[66],[20,7507],{"className":7508,"style":1578},[70],[20,7510,7512,7515],{"className":7511},[75],[20,7513,41],{"className":7514,"style":77},[75,76],[20,7516,7518],{"className":7517},[550],[20,7519,7521],{"className":7520},[396],[20,7522,7524],{"className":7523},[401],[20,7525,7527],{"className":7526,"style":1597},[405],[20,7528,7529,7532],{"style":1600},[20,7530],{"className":7531,"style":567},[413],[20,7533,7535],{"className":7534},[448,449,450,451],[20,7536,7538],{"className":7537},[75,451],[20,7539,330],{"className":7540},[75,451],[20,7542,46],{"className":7543},[81],[20,7545,2526],{"className":7546,"style":1196},[75,76],[20,7548,46],{"className":7549},[81],[20,7551,49],{"className":7552},[75,76],[20,7554,917],{"className":7555},[88],[20,7557],{"className":7558,"style":1759},[134],[20,7560,7416],{"className":7561},[461],[20,7563],{"className":7564,"style":1759},[134],[20,7566,7568,7571,7603,7606,7609],{"className":7567},[66],[20,7569],{"className":7570,"style":1578},[70],[20,7572,7574,7577],{"className":7573},[75],[20,7575,2526],{"className":7576,"style":1196},[75,76],[20,7578,7580],{"className":7579},[550],[20,7581,7583],{"className":7582},[396],[20,7584,7586],{"className":7585},[401],[20,7587,7589],{"className":7588,"style":1597},[405],[20,7590,7591,7594],{"style":1600},[20,7592],{"className":7593,"style":567},[413],[20,7595,7597],{"className":7596},[448,449,450,451],[20,7598,7600],{"className":7599},[75,451],[20,7601,330],{"className":7602},[75,451],[20,7604,46],{"className":7605},[81],[20,7607,49],{"className":7608},[75,76],[20,7610,52],{"className":7611},[88],[20,7613,7615],{"className":7614},[251],[20,7616,7618,7665],{"className":7617},[23],[20,7619,7621],{"className":7620},[27],[29,7622,7623],{"xmlns":31,"display":260},[33,7624,7625,7662],{},[36,7626,7627,7642,7644],{},[287,7628,7629,7636],{},[36,7630,7631,7634],{},[39,7632,7633],{},"d",[39,7635,49],{},[36,7637,7638,7640],{},[39,7639,7633],{},[39,7641,1169],{},[43,7643,320],{},[287,7645,7646,7648],{},[1535,7647,4665],{},[287,7649,7650,7656],{},[36,7651,7652,7654],{},[39,7653,7633],{},[39,7655,1169],{},[36,7657,7658,7660],{},[39,7659,7633],{},[39,7661,49],{},[54,7663,7664],{"encoding":56},"\\frac{dx}{dy} = \\frac{1}{\\frac{dy}{dx}}",[20,7666,7668,7754],{"className":7667,"ariaHidden":62},[61],[20,7669,7671,7675,7745,7748,7751],{"className":7670},[66],[20,7672],{"className":7673,"style":7674},[70],"height:2.2519em;vertical-align:-0.8804em;",[20,7676,7678,7681,7742],{"className":7677},[75],[20,7679],{"className":7680},[81,424],[20,7682,7684],{"className":7683},[287],[20,7685,7687,7733],{"className":7686},[396,397],[20,7688,7690,7730],{"className":7689},[401],[20,7691,7694,7708,7716],{"className":7692,"style":7693},[405],"height:1.3714em;",[20,7695,7696,7699],{"style":1720},[20,7697],{"className":7698,"style":444},[413],[20,7700,7702,7705],{"className":7701},[75],[20,7703,7633],{"className":7704},[75,76],[20,7706,1169],{"className":7707,"style":1196},[75,76],[20,7709,7710,7713],{"style":467},[20,7711],{"className":7712,"style":444},[413],[20,7714],{"className":7715,"style":475},[474],[20,7717,7718,7721],{"style":1740},[20,7719],{"className":7720,"style":444},[413],[20,7722,7724,7727],{"className":7723},[75],[20,7725,7633],{"className":7726},[75,76],[20,7728,49],{"className":7729},[75,76],[20,7731,519],{"className":7732},[518],[20,7734,7736],{"className":7735},[401],[20,7737,7740],{"className":7738,"style":7739},[405],"height:0.8804em;",[20,7741],{},[20,7743],{"className":7744},[88,424],[20,7746],{"className":7747,"style":135},[134],[20,7749,320],{"className":7750},[139],[20,7752],{"className":7753,"style":135},[134],[20,7755,7757,7761],{"className":7756},[66],[20,7758],{"className":7759,"style":7760},[70],"height:2.4887em;vertical-align:-1.1672em;",[20,7762,7764,7767,7896],{"className":7763},[75],[20,7765],{"className":7766},[81,424],[20,7768,7770],{"className":7769},[287],[20,7771,7773,7887],{"className":7772},[396,397],[20,7774,7776,7884],{"className":7775},[401],[20,7777,7779,7865,7873],{"className":7778,"style":4769},[405],[20,7780,7782,7785],{"style":7781},"top:-2.1778em;",[20,7783],{"className":7784,"style":444},[413],[20,7786,7788],{"className":7787},[75],[20,7789,7791,7794,7862],{"className":7790},[75],[20,7792],{"className":7793},[81,424],[20,7795,7797],{"className":7796},[287],[20,7798,7800,7853],{"className":7799},[396,397],[20,7801,7803,7850],{"className":7802},[401],[20,7804,7807,7824,7832],{"className":7805,"style":7806},[405],"height:0.9322em;",[20,7808,7809,7812],{"style":440},[20,7810],{"className":7811,"style":444},[413],[20,7813,7815],{"className":7814},[448,449,450,451],[20,7816,7818,7821],{"className":7817},[75,451],[20,7819,7633],{"className":7820},[75,76,451],[20,7822,49],{"className":7823},[75,76,451],[20,7825,7826,7829],{"style":467},[20,7827],{"className":7828,"style":444},[413],[20,7830],{"className":7831,"style":475},[474],[20,7833,7835,7838],{"style":7834},"top:-3.4461em;",[20,7836],{"className":7837,"style":444},[413],[20,7839,7841],{"className":7840},[448,449,450,451],[20,7842,7844,7847],{"className":7843},[75,451],[20,7845,7633],{"className":7846},[75,76,451],[20,7848,1169],{"className":7849,"style":1196},[75,76,451],[20,7851,519],{"className":7852},[518],[20,7854,7856],{"className":7855},[401],[20,7857,7860],{"className":7858,"style":7859},[405],"height:0.345em;",[20,7861],{},[20,7863],{"className":7864},[88,424],[20,7866,7867,7870],{"style":467},[20,7868],{"className":7869,"style":444},[413],[20,7871],{"className":7872,"style":475},[474],[20,7874,7875,7878],{"style":1740},[20,7876],{"className":7877,"style":444},[413],[20,7879,7881],{"className":7880},[75],[20,7882,4665],{"className":7883},[75],[20,7885,519],{"className":7886},[518],[20,7888,7890],{"className":7889},[401],[20,7891,7894],{"className":7892,"style":7893},[405],"height:1.1672em;",[20,7895],{},[20,7897],{"className":7898},[88,424],[20,7900,7902],{"className":7901},[251],[20,7903,7905,7964],{"className":7904},[23],[20,7906,7908],{"className":7907},[27],[29,7909,7910],{"xmlns":31,"display":260},[33,7911,7912,7961],{},[36,7913,7914,7928,7930,7945,7947],{},[287,7915,7916,7922],{},[36,7917,7918,7920],{},[39,7919,7633],{},[39,7921,1169],{},[36,7923,7924,7926],{},[39,7925,7633],{},[39,7927,49],{},[43,7929,320],{},[287,7931,7932,7938],{},[36,7933,7934,7936],{},[39,7935,7633],{},[39,7937,1169],{},[36,7939,7940,7942],{},[39,7941,7633],{},[39,7943,7944],{},"u",[43,7946,7416],{},[287,7948,7949,7955],{},[36,7950,7951,7953],{},[39,7952,7633],{},[39,7954,7944],{},[36,7956,7957,7959],{},[39,7958,7633],{},[39,7960,49],{},[54,7962,7963],{"encoding":56},"\\frac{dy}{dx} = \\frac{dy}{du} \\cdot 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= \\frac{ \\frac{dy}{d \\theta} }{ \\frac{dx}{d \\theta} 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= (\\frac{d^2 x}{dt^2}, \\frac{d^2 y}{dt^2})",[20,10640,10642,10692],{"className":10641,"ariaHidden":62},[61],[20,10643,10645,10648,10683,10686,10689],{"className":10644},[66],[20,10646],{"className":10647,"style":10347},[70],[20,10649,10651],{"className":10650},[75,10351],[20,10652,10654],{"className":10653},[396],[20,10655,10657],{"className":10656},[401],[20,10658,10660,10668],{"className":10659,"style":10347},[405],[20,10661,10662,10665],{"style":1675},[20,10663],{"className":10664,"style":444},[413],[20,10666,4932],{"className":10667,"style":4948},[75,76],[20,10669,10670,10673],{"style":1675},[20,10671],{"className":10672,"style":444},[413],[20,10674,10676],{"className":10675,"style":10378},[10377],[20,10677,10679],{"className":10678,"style":10383},[10382],[10385,10680,10681],{"xmlns":10387,"width":10388,"height":10389,"style":10390,"viewBox":10391,"preserveAspectRatio":10392},[10394,10682],{"d":10396},[20,10684],{"className":10685,"style":135},[134],[20,10687,320],{"className":10688},[139],[20,10690],{"className":10691,"style":135},[134],[20,10693,10695,10699,10702,10824,10827,10830,10950],{"className":10694},[66],[20,10696],{"className":10697,"style":10698},[70],"height:2.1771em;vertical-align:-0.686em;",[20,10700,46],{"className":10701},[81],[20,10703,10705,10708,10821],{"className":10704},[75],[20,10706],{"className":10707},[81,424],[20,10709,10711],{"className":10710},[287],[20,10712,10714,10813],{"className":10713},[396,397],[20,10715,10717,10810],{"className":10716},[401],[20,10718,10721,10761,10769],{"className":10719,"style":10720},[405],"height:1.4911em;",[20,10722,10723,10726],{"style":1720},[20,10724],{"className":10725,"style":444},[413],[20,10727,10729,10732],{"className":10728},[75],[20,10730,7633],{"className":10731},[75,76],[20,10733,10735,10738],{"className":10734},[75],[20,10736,10316],{"className":10737},[75,76],[20,10739,10741],{"className":10740},[550],[20,10742,10744],{"className":10743},[396],[20,10745,10747],{"className":10746},[401],[20,10748,10750],{"className":10749,"style":6833},[405],[20,10751,10752,10755],{"style":4799},[20,10753],{"className":10754,"style":567},[413],[20,10756,10758],{"className":10757},[448,449,450,451],[20,10759,6617],{"className":10760},[75,451],[20,10762,10763,10766],{"style":467},[20,10764],{"className":10765,"style":444},[413],[20,10767],{"className":10768,"style":475},[474],[20,10770,10771,10774],{"style":1740},[20,10772],{"className":10773,"style":444},[413],[20,10775,10777,10807],{"className":10776},[75],[20,10778,10780,10783],{"className":10779},[75],[20,10781,7633],{"className":10782},[75,76],[20,10784,10786],{"className":10785},[550],[20,10787,10789],{"className":10788},[396],[20,10790,10792],{"className":10791},[401],[20,10793,10796],{"className":10794,"style":10795},[405],"height:0.8141em;",[20,10797,10798,10801],{"style":563},[20,10799],{"className":10800,"style":567},[413],[20,10802,10804],{"className":10803},[448,449,450,451],[20,10805,6617],{"className":10806},[75,451],[20,10808,49],{"className":10809},[75,76],[20,10811,519],{"className":10812},[518],[20,10814,10816],{"className":10815},[401],[20,10817,10819],{"className":10818,"style":1802},[405],[20,10820],{},[20,10822],{"className":10823},[88,424],[20,10825,868],{"className":10826},[900],[20,10828],{"className":10829,"style":904},[134],[20,10831,10833,10836,10947],{"className":10832},[75],[20,10834],{"className":10835},[81,424],[20,10837,10839],{"className":10838},[287],[20,10840,10842,10939],{"className":10841},[396,397],[20,10843,10845,10936],{"className":10844},[401],[20,10846,10848,10888,10896],{"className":10847,"style":10720},[405],[20,10849,10850,10853],{"style":1720},[20,10851],{"className":10852,"style":444},[413],[20,10854,10856,10859],{"className":10855},[75],[20,10857,7633],{"className":10858},[75,76],[20,10860,10862,10865],{"className":10861},[75],[20,10863,10316],{"className":10864},[75,76],[20,10866,10868],{"className":10867},[550],[20,10869,10871],{"className":10870},[396],[20,10872,10874],{"className":10873},[401],[20,10875,10877],{"className":10876,"style":6833},[405],[20,10878,10879,10882],{"style":4799},[20,10880],{"className":10881,"style":567},[413],[20,10883,10885],{"className":10884},[448,449,450,451],[20,10886,6617],{"className":10887},[75,451],[20,10889,10890,10893],{"style":467},[20,10891],{"className":10892,"style":444},[413],[20,10894],{"className":10895,"style":475},[474],[20,10897,10898,10901],{"style":1740},[20,10899],{"className":10900,"style":444},[413],[20,10902,10904,10933],{"className":10903},[75],[20,10905,10907,10910],{"className":10906},[75],[20,10908,7633],{"className":10909},[75,76],[20,10911,10913],{"className":10912},[550],[20,10914,10916],{"className":10915},[396],[20,10917,10919],{"className":10918},[401],[20,10920,10922],{"className":10921,"style":10795},[405],[20,10923,10924,10927],{"style":563},[20,10925],{"className":10926,"style":567},[413],[20,10928,10930],{"className":10929},[448,449,450,451],[20,10931,6617],{"className":10932},[75,451],[20,10934,1169],{"className":10935,"style":1196},[75,76],[20,10937,519],{"className":10938},[518],[20,10940,10942],{"className":10941},[401],[20,10943,10945],{"className":10944,"style":1802},[405],[20,10946],{},[20,10948],{"className":10949},[88,424],[20,10951,52],{"className":10952},[88],{"title":1129,"searchDepth":1130,"depth":1130,"links":10954},[10955],{"id":10269,"depth":1130,"text":10270},{},"\u002Fdict\u002Fdifferential-velocity",{"title":10264,"description":1129},"dict\u002Fdifferential-velocity\u002Findex","HJDiIPC6gL6ZEj6cPZYXx6HG1DXF4ovjqYZGvNKI5-c","\u002Fcontent\u002Fdifferential-velocity",{"id":10963,"title":10964,"body":10965,"category":1134,"description":1129,"draft":1135,"extension":1136,"meta":11802,"navigation":1138,"path":11803,"seo":11804,"stem":11805,"__hash__":11806,"actualPath":11807},"dictionary\u002Fdict\u002Ffirst-order-approximation\u002Findex.md","一次近似",{"type":8,"value":10966,"toc":11796},[10967,10969,10972,10976,11168,11171,11363,11366,11369,11424,11491,11558,11652],[11,10968,2824],{"id":2823},[16,10970,10971],{},"「複雑なグラフも，一部だけ拡大して見ると直線に見える」と言うイメージ．",[11,10973,10975],{"id":10974},"_2-一次近似","2. 一次近似",[20,10977,10979],{"className":10978},[251],[20,10980,10982,11037],{"className":10981},[23],[20,10983,10985],{"className":10984},[27],[29,10986,10987],{"xmlns":31,"display":260},[33,10988,10989,11034],{},[36,10990,10991,10993,10995,10997,10999,11002,11004,11006,11008,11010,11012,11018,11020,11022,11024,11026,11028,11030,11032],{},[39,10992,41],{},[43,10994,46],{"stretchy":45},[39,10996,49],{},[43,10998,52],{"stretchy":45},[43,11000,11001],{},"≈",[39,11003,41],{},[43,11005,46],{"stretchy":45},[39,11007,104],{},[43,11009,52],{"stretchy":45},[43,11011,1549],{},[322,11013,11014,11016],{},[39,11015,41],{},[43,11017,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,11019,46],{"stretchy":45},[39,11021,104],{},[43,11023,52],{"stretchy":45},[43,11025,46],{"stretchy":45},[39,11027,49],{},[43,11029,301],{},[39,11031,104],{},[43,11033,52],{"stretchy":45},[54,11035,11036],{"encoding":56},"f(x) \\approx f(a) + f'(a)(x-a)",[20,11038,11040,11067,11094,11156],{"className":11039,"ariaHidden":62},[61],[20,11041,11043,11046,11049,11052,11055,11058,11061,11064],{"className":11042},[66],[20,11044],{"className":11045,"style":71},[70],[20,11047,41],{"className":11048,"style":77},[75,76],[20,11050,46],{"className":11051},[81],[20,11053,49],{"className":11054},[75,76],[20,11056,52],{"className":11057},[88],[20,11059],{"className":11060,"style":135},[134],[20,11062,11001],{"className":11063},[139],[20,11065],{"className":11066,"style":135},[134],[20,11068,11070,11073,11076,11079,11082,11085,11088,11091],{"className":11069},[66],[20,11071],{"className":11072,"style":71},[70],[20,11074,41],{"className":11075,"style":77},[75,76],[20,11077,46],{"className":11078},[81],[20,11080,104],{"className":11081},[75,76],[20,11083,52],{"className":11084},[88],[20,11086],{"className":11087,"style":1759},[134],[20,11089,1549],{"className":11090},[461],[20,11092],{"className":11093,"style":1759},[134],[20,11095,11097,11100,11132,11135,11138,11141,11144,11147,11150,11153],{"className":11096},[66],[20,11098],{"className":11099,"style":1578},[70],[20,11101,11103,11106],{"className":11102},[75],[20,11104,41],{"className":11105,"style":77},[75,76],[20,11107,11109],{"className":11108},[550],[20,11110,11112],{"className":11111},[396],[20,11113,11115],{"className":11114},[401],[20,11116,11118],{"className":11117,"style":1597},[405],[20,11119,11120,11123],{"style":1600},[20,11121],{"className":11122,"style":567},[413],[20,11124,11126],{"className":11125},[448,449,450,451],[20,11127,11129],{"className":11128},[75,451],[20,11130,330],{"className":11131},[75,451],[20,11133,46],{"className":11134},[81],[20,11136,104],{"className":11137},[75,76],[20,11139,52],{"className":11140},[88],[20,11142,46],{"className":11143},[81],[20,11145,49],{"className":11146},[75,76],[20,11148],{"className":11149,"style":1759},[134],[20,11151,301],{"className":11152},[461],[20,11154],{"className":11155,"style":1759},[134],[20,11157,11159,11162,11165],{"className":11158},[66],[20,11160],{"className":11161,"style":71},[70],[20,11163,104],{"className":11164},[75,76],[20,11166,52],{"className":11167},[88],[16,11169,11170],{},"尚，",[5577,11172,11173,11220,11299],{},[690,11174,11175,11219],{},[20,11176,11178,11198],{"className":11177},[23],[20,11179,11181],{"className":11180},[27],[29,11182,11183],{"xmlns":31},[33,11184,11185,11195],{},[36,11186,11187,11189,11191,11193],{},[39,11188,41],{},[43,11190,46],{"stretchy":45},[39,11192,104],{},[43,11194,52],{"stretchy":45},[54,11196,11197],{"encoding":56},"f(a)",[20,11199,11201],{"className":11200,"ariaHidden":62},[61],[20,11202,11204,11207,11210,11213,11216],{"className":11203},[66],[20,11205],{"className":11206,"style":71},[70],[20,11208,41],{"className":11209,"style":77},[75,76],[20,11211,46],{"className":11212},[81],[20,11214,104],{"className":11215},[75,76],[20,11217,52],{"className":11218},[88]," ：基準となる点の値",[690,11221,11222,11298],{},[20,11223,11225,11248],{"className":11224},[23],[20,11226,11228],{"className":11227},[27],[29,11229,11230],{"xmlns":31},[33,11231,11232,11246],{},[36,11233,11234,11240,11242,11244],{},[322,11235,11236,11238],{},[39,11237,41],{},[43,11239,330],{"mathvariant":328,"lspace":329,"rspace":329},[43,11241,46],{"stretchy":45},[39,11243,104],{},[43,11245,52],{"stretchy":45},[54,11247,1309],{"encoding":56},[20,11249,11251],{"className":11250,"ariaHidden":62},[61],[20,11252,11254,11257,11289,11292,11295],{"className":11253},[66],[20,11255],{"className":11256,"style":1026},[70],[20,11258,11260,11263],{"className":11259},[75],[20,11261,41],{"className":11262,"style":77},[75,76],[20,11264,11266],{"className":11265},[550],[20,11267,11269],{"className":11268},[396],[20,11270,11272],{"className":11271},[401],[20,11273,11275],{"className":11274,"style":560},[405],[20,11276,11277,11280],{"style":563},[20,11278],{"className":11279,"style":567},[413],[20,11281,11283],{"className":11282},[448,449,450,451],[20,11284,11286],{"className":11285},[75,451],[20,11287,330],{"className":11288},[75,451],[20,11290,46],{"className":11291},[81],[20,11293,104],{"className":11294},[75,76],[20,11296,52],{"className":11297},[88]," ：その点における傾き（微分係数）",[690,11300,11301,11362],{},[20,11302,11304,11326],{"className":11303},[23],[20,11305,11307],{"className":11306},[27],[29,11308,11309],{"xmlns":31},[33,11310,11311,11323],{},[36,11312,11313,11315,11317,11319,11321],{},[43,11314,46],{"stretchy":45},[39,11316,49],{},[43,11318,301],{},[39,11320,104],{},[43,11322,52],{"stretchy":45},[54,11324,11325],{"encoding":56},"(x−a)",[20,11327,11329,11350],{"className":11328,"ariaHidden":62},[61],[20,11330,11332,11335,11338,11341,11344,11347],{"className":11331},[66],[20,11333],{"className":11334,"style":71},[70],[20,11336,46],{"className":11337},[81],[20,11339,49],{"className":11340},[75,76],[20,11342],{"className":11343,"style":1759},[134],[20,11345,301],{"className":11346},[461],[20,11348],{"className":11349,"style":1759},[134],[20,11351,11353,11356,11359],{"className":11352},[66],[20,11354],{"className":11355,"style":71},[70],[20,11357,104],{"className":11358},[75,76],[20,11360,52],{"className":11361},[88]," ：基準点からの微小なズレ（変化量）",[16,11364,11365],{},"であるから，「元の値に，（傾き × ズレ）を足したもの」で大体の値を予想するものである．",[4883,11367,11368],{"id":11368},"具体例",[16,11370,11371,11423],{},[20,11372,11374,11392],{"className":11373},[23],[20,11375,11377],{"className":11376},[27],[29,11378,11379],{"xmlns":31},[33,11380,11381,11389],{},[36,11382,11383,11385,11387],{},[39,11384,49],{},[43,11386,11001],{},[1535,11388,283],{},[54,11390,11391],{"encoding":56},"x \\approx 0",[20,11393,11395,11414],{"className":11394,"ariaHidden":62},[61],[20,11396,11398,11402,11405,11408,11411],{"className":11397},[66],[20,11399],{"className":11400,"style":11401},[70],"height:0.4831em;",[20,11403,49],{"className":11404},[75,76],[20,11406],{"className":11407,"style":135},[134],[20,11409,11001],{"className":11410},[139],[20,11412],{"className":11413,"style":135},[134],[20,11415,11417,11420],{"className":11416},[66],[20,11418],{"className":11419,"style":4173},[70],[20,11421,283],{"className":11422},[75]," のとき，",[20,11425,11427],{"className":11426},[251],[20,11428,11430,11452],{"className":11429},[23],[20,11431,11433],{"className":11432},[27],[29,11434,11435],{"xmlns":31,"display":260},[33,11436,11437,11449],{},[36,11438,11439,11441,11443,11445,11447],{},[39,11440,9001],{},[43,11442,1525],{},[39,11444,49],{},[43,11446,11001],{},[39,11448,49],{},[54,11450,11451],{"encoding":56},"\\sin{x} \\approx x",[20,11453,11455,11482],{"className":11454,"ariaHidden":62},[61],[20,11456,11458,11461,11464,11467,11473,11476,11479],{"className":11457},[66],[20,11459],{"className":11460,"style":9018},[70],[20,11462,9001],{"className":11463},[1641],[20,11465],{"className":11466,"style":904},[134],[20,11468,11470],{"className":11469},[75],[20,11471,49],{"className":11472},[75,76],[20,11474],{"className":11475,"style":135},[134],[20,11477,11001],{"className":11478},[139],[20,11480],{"className":11481,"style":135},[134],[20,11483,11485,11488],{"className":11484},[66],[20,11486],{"className":11487,"style":665},[70],[20,11489,49],{"className":11490},[75,76],[20,11492,11494],{"className":11493},[251],[20,11495,11497,11519],{"className":11496},[23],[20,11498,11500],{"className":11499},[27],[29,11501,11502],{"xmlns":31,"display":260},[33,11503,11504,11516],{},[36,11505,11506,11508,11510,11512,11514],{},[39,11507,9044],{},[43,11509,1525],{},[39,11511,49],{},[43,11513,11001],{},[1535,11515,4665],{},[54,11517,11518],{"encoding":56},"\\cos{x} \\approx 1",[20,11520,11522,11549],{"className":11521,"ariaHidden":62},[61],[20,11523,11525,11528,11531,11534,11540,11543,11546],{"className":11524},[66],[20,11526],{"className":11527,"style":11401},[70],[20,11529,9044],{"className":11530},[1641],[20,11532],{"className":11533,"style":904},[134],[20,11535,11537],{"className":11536},[75],[20,11538,49],{"className":11539},[75,76],[20,11541],{"className":11542,"style":135},[134],[20,11544,11001],{"className":11545},[139],[20,11547],{"className":11548,"style":135},[134],[20,11550,11552,11555],{"className":11551},[66],[20,11553],{"className":11554,"style":4173},[70],[20,11556,4665],{"className":11557},[75],[20,11559,11561],{"className":11560},[251],[20,11562,11564,11595],{"className":11563},[23],[20,11565,11567],{"className":11566},[27],[29,11568,11569],{"xmlns":31,"display":260},[33,11570,11571,11592],{},[36,11572,11573,11576,11578,11580,11582,11584,11586,11588,11590],{},[39,11574,11575],{},"ln",[43,11577,1525],{},[43,11579,46],{"stretchy":45},[39,11581,104],{},[43,11583,1549],{},[39,11585,49],{},[43,11587,52],{"stretchy":45},[43,11589,11001],{},[39,11591,49],{},[54,11593,11594],{"encoding":56},"\\ln (a + x) \\approx x",[20,11596,11598,11622,11643],{"className":11597,"ariaHidden":62},[61],[20,11599,11601,11604,11607,11610,11613,11616,11619],{"className":11600},[66],[20,11602],{"className":11603,"style":71},[70],[20,11605,11575],{"className":11606},[1641],[20,11608,46],{"className":11609},[81],[20,11611,104],{"className":11612},[75,76],[20,11614],{"className":11615,"style":1759},[134],[20,11617,1549],{"className":11618},[461],[20,11620],{"className":11621,"style":1759},[134],[20,11623,11625,11628,11631,11634,11637,11640],{"className":11624},[66],[20,11626],{"className":11627,"style":71},[70],[20,11629,49],{"className":11630},[75,76],[20,11632,52],{"className":11633},[88],[20,11635],{"className":11636,"style":135},[134],[20,11638,11001],{"className":11639},[139],[20,11641],{"className":11642,"style":135},[134],[20,11644,11646,11649],{"className":11645},[66],[20,11647],{"className":11648,"style":665},[70],[20,11650,49],{"className":11651},[75,76],[20,11653,11655],{"className":11654},[251],[20,11656,11658,11694],{"className":11657},[23],[20,11659,11661],{"className":11660},[27],[29,11662,11663],{"xmlns":31,"display":260},[33,11664,11665,11691],{},[36,11666,11667,11669,11671,11673,11675,11681,11683,11685,11687,11689],{},[43,11668,46],{"stretchy":45},[1535,11670,4665],{},[43,11672,1549],{},[39,11674,49],{},[322,11676,11677,11679],{},[43,11678,52],{"stretchy":45},[39,11680,6019],{},[43,11682,11001],{},[1535,11684,4665],{},[43,11686,1549],{},[39,11688,6019],{},[39,11690,49],{},[54,11692,11693],{"encoding":56},"(1 + x) ^ n \\approx 1 + nx",[20,11695,11697,11718,11765,11784],{"className":11696,"ariaHidden":62},[61],[20,11698,11700,11703,11706,11709,11712,11715],{"className":11699},[66],[20,11701],{"className":11702,"style":71},[70],[20,11704,46],{"className":11705},[81],[20,11707,4665],{"className":11708},[75],[20,11710],{"className":11711,"style":1759},[134],[20,11713,1549],{"className":11714},[461],[20,11716],{"className":11717,"style":1759},[134],[20,11719,11721,11724,11727,11756,11759,11762],{"className":11720},[66],[20,11722],{"className":11723,"style":71},[70],[20,11725,49],{"className":11726},[75,76],[20,11728,11730,11733],{"className":11729},[88],[20,11731,52],{"className":11732},[88],[20,11734,11736],{"className":11735},[550],[20,11737,11739],{"className":11738},[396],[20,11740,11742],{"className":11741},[401],[20,11743,11745],{"className":11744,"style":6086},[405],[20,11746,11747,11750],{"style":1600},[20,11748],{"className":11749,"style":567},[413],[20,11751,11753],{"className":11752},[448,449,450,451],[20,11754,6019],{"className":11755},[75,76,451],[20,11757],{"className":11758,"style":135},[134],[20,11760,11001],{"className":11761},[139],[20,11763],{"className":11764,"style":135},[134],[20,11766,11768,11772,11775,11778,11781],{"className":11767},[66],[20,11769],{"className":11770,"style":11771},[70],"height:0.7278em;vertical-align:-0.0833em;",[20,11773,4665],{"className":11774},[75],[20,11776],{"className":11777,"style":1759},[134],[20,11779,1549],{"className":11780},[461],[20,11782],{"className":11783,"style":1759},[134],[20,11785,11787,11790,11793],{"className":11786},[66],[20,11788],{"className":11789,"style":665},[70],[20,11791,6019],{"className":11792},[75,76],[20,11794,49],{"className":11795},[75,76],{"title":1129,"searchDepth":1130,"depth":1130,"links":11797},[11798,11799],{"id":2823,"depth":1130,"text":2824},{"id":10974,"depth":1130,"text":10975,"children":11800},[11801],{"id":11368,"depth":5234,"text":11368},{},"\u002Fdict\u002Ffirst-order-approximation",{"title":10964,"description":1129},"dict\u002Ffirst-order-approximation\u002Findex","fi5zOVp5opWuuq6X20b9WAZHvHskg2WjFi-kmwExzOE","\u002Fcontent\u002Ffirst-order-approximation",1779282662545]