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Für spezielle Exponenten reicht weniger: Bei natürlichen Zahlen gilt die Regel für alle ",[574,1033,1035,1048],{"className":1034},[577],[574,1036,1038],{"className":1037},[581],[583,1039,1040],{"xmlns":585},[587,1041,1042,1046],{},[590,1043,1044],{},[593,1045,891],{},[597,1047,891],{"encoding":599},[574,1049,1051],{"className":1050,"ariaHidden":604},[603],[574,1052,1054,1057],{"className":1053},[608],[574,1055],{"className":1056,"style":613},[612],[574,1058,891],{"className":1059},[617,618],", bei negativen ganzen Zahlen für ",[574,1062,1064,1084],{"className":1063},[577],[574,1065,1067],{"className":1066},[581],[583,1068,1069],{"xmlns":585},[587,1070,1071,1081],{},[590,1072,1073,1075,1079],{},[593,1074,891],{},[893,1076,1078],{"mathvariant":1077},"normal","≠",[637,1080,898],{},[597,1082,1083],{"encoding":599},"x \\neq 0",[574,1085,1087,1147],{"className":1086,"ariaHidden":604},[603],[574,1088,1090,1094,1097,1100,1144],{"className":1089},[608],[574,1091],{"className":1092,"style":1093},[612],"height:0.8889em;vertical-align:-0.1944em;",[574,1095,891],{"className":1096},[617,618],[574,1098],{"className":1099,"style":919},[918],[574,1101,1103,1136,1140],{"className":1102},[923],[574,1104,1106],{"className":1105},[923],[574,1107,1110],{"className":1108},[617,1109],"vbox",[574,1111,1114],{"className":1112},[1113],"thinbox",[574,1115,1118,1121,1132],{"className":1116},[1117],"rlap",[574,1119],{"className":1120,"style":1093},[612],[574,1122,1125],{"className":1123},[1124],"inner",[574,1126,1128],{"className":1127},[617],[574,1129,1131],{"className":1130},[923],"",[574,1133],{"className":1134},[1135],"fix",[574,1137],{"className":1138},[918,1139],"nobreak",[574,1141,1143],{"className":1142},[923],"=",[574,1145],{"className":1146,"style":919},[918],[574,1148,1150,1153],{"className":1149},[608],[574,1151],{"className":1152,"style":933},[612],[574,1154,898],{"className":1155},[617],[565,1157,1158],{},"Wichtig ist die Unterscheidung:",[1160,1161,1162,1228,1479],"ul",{},[1163,1164,1165,1223,1224,1227],"li",{},[574,1166,1168,1185],{"className":1167},[577],[574,1169,1171],{"className":1170},[581],[583,1172,1173],{"xmlns":585},[587,1174,1175,1183],{},[590,1176,1177],{},[951,1178,1179,1181],{},[593,1180,891],{},[593,1182,595],{},[597,1184,959],{"encoding":599},[574,1186,1188],{"className":1187,"ariaHidden":604},[603],[574,1189,1191,1194],{"className":1190},[608],[574,1192],{"className":1193,"style":969},[612],[574,1195,1197,1200],{"className":1196},[617],[574,1198,891],{"className":1199},[617,618],[574,1201,1203],{"className":1202},[979],[574,1204,1206],{"className":1205},[670],[574,1207,1209],{"className":1208},[675],[574,1210,1212],{"className":1211,"style":969},[679],[574,1213,1214,1217],{"style":991},[574,1215],{"className":1216,"style":995},[687],[574,1218,1220],{"className":1219},[692,693,694,695],[574,1221,595],{"className":1222,"style":619},[617,618,695],": Die ",[569,1225,1226],{},"Basis"," ist variabel, der Exponent fest. Hier gilt diese Regel.",[1163,1229,1230,1290,1291,1294,1295,873],{},[574,1231,1233,1252],{"className":1232},[577],[574,1234,1236],{"className":1235},[581],[583,1237,1238],{"xmlns":585},[587,1239,1240,1249],{},[590,1241,1242],{},[951,1243,1244,1247],{},[593,1245,1246],{},"a",[593,1248,891],{},[597,1250,1251],{"encoding":599},"a^x",[574,1253,1255],{"className":1254,"ariaHidden":604},[603],[574,1256,1258,1261],{"className":1257},[608],[574,1259],{"className":1260,"style":969},[612],[574,1262,1264,1267],{"className":1263},[617],[574,1265,1246],{"className":1266},[617,618],[574,1268,1270],{"className":1269},[979],[574,1271,1273],{"className":1272},[670],[574,1274,1276],{"className":1275},[675],[574,1277,1279],{"className":1278,"style":969},[679],[574,1280,1281,1284],{"style":991},[574,1282],{"className":1283,"style":995},[687],[574,1285,1287],{"className":1286},[692,693,694,695],[574,1288,891],{"className":1289},[617,618,695],": Der ",[569,1292,1293],{},"Exponent"," ist variabel. Das ist eine Exponentialfunktion mit ",[574,1296,1298,1345],{"className":1297},[577],[574,1299,1301],{"className":1300},[581],[583,1302,1303],{"xmlns":585},[587,1304,1305,1342],{},[590,1306,1307,1311,1317,1326,1328,1334,1337,1340],{},[893,1308,1310],{"stretchy":1309},"false","(",[951,1312,1313,1315],{},[593,1314,1246],{},[593,1316,891],{},[951,1318,1319,1322],{},[893,1320,1321],{"stretchy":1309},")",[893,1323,1325],{"mathvariant":1077,"lspace":1324,"rspace":1324},"0em","′",[893,1327,1143],{},[951,1329,1330,1332],{},[593,1331,1246],{},[593,1333,891],{},[593,1335,1336],{},"ln",[893,1338,1339],{},"⁡",[593,1341,1246],{},[597,1343,1344],{"encoding":599},"(a^x)' = a^x \\ln a",[574,1346,1348,1429],{"className":1347,"ariaHidden":604},[603],[574,1349,1351,1355,1358,1387,1420,1423,1426],{"className":1350},[608],[574,1352],{"className":1353,"style":1354},[612],"height:1.0019em;vertical-align:-0.25em;",[574,1356,1310],{"className":1357},[662],[574,1359,1361,1364],{"className":1360},[617],[574,1362,1246],{"className":1363},[617,618],[574,1365,1367],{"className":1366},[979],[574,1368,1370],{"className":1369},[670],[574,1371,1373],{"className":1372},[675],[574,1374,1376],{"className":1375,"style":969},[679],[574,1377,1378,1381],{"style":991},[574,1379],{"className":1380,"style":995},[687],[574,1382,1384],{"className":1383},[692,693,694,695],[574,1385,891],{"className":1386},[617,618,695],[574,1388,1390,1393],{"className":1389},[745],[574,1391,1321],{"className":1392},[745],[574,1394,1396],{"className":1395},[979],[574,1397,1399],{"className":1398},[670],[574,1400,1402],{"className":1401},[675],[574,1403,1406],{"className":1404,"style":1405},[679],"height:0.7519em;",[574,1407,1408,1411],{"style":991},[574,1409],{"className":1410,"style":995},[687],[574,1412,1414],{"className":1413},[692,693,694,695],[574,1415,1417],{"className":1416},[617,695],[574,1418,1325],{"className":1419},[617,695],[574,1421],{"className":1422,"style":919},[918],[574,1424,1143],{"className":1425},[923],[574,1427],{"className":1428,"style":919},[918],[574,1430,1432,1436,1465,1469,1473,1476],{"className":1431},[608],[574,1433],{"className":1434,"style":1435},[612],"height:0.6944em;",[574,1437,1439,1442],{"className":1438},[617],[574,1440,1246],{"className":1441},[617,618],[574,1443,1445],{"className":1444},[979],[574,1446,1448],{"className":1447},[670],[574,1449,1451],{"className":1450},[675],[574,1452,1454],{"className":1453,"style":969},[679],[574,1455,1456,1459],{"style":991},[574,1457],{"className":1458,"style":995},[687],[574,1460,1462],{"className":1461},[692,693,694,695],[574,1463,891],{"className":1464},[617,618,695],[574,1466],{"className":1467,"style":1468},[918],"margin-right:0.1667em;",[574,1470,1336],{"className":1471},[1472],"mop",[574,1474],{"className":1475,"style":1468},[918],[574,1477,1246],{"className":1478},[617,618],[1163,1480,1481,1540,1541,873],{},[574,1482,1484,1502],{"className":1483},[577],[574,1485,1487],{"className":1486},[581],[583,1488,1489],{"xmlns":585},[587,1490,1491,1499],{},[590,1492,1493],{},[951,1494,1495,1497],{},[593,1496,891],{},[593,1498,891],{},[597,1500,1501],{"encoding":599},"x^x",[574,1503,1505],{"className":1504,"ariaHidden":604},[603],[574,1506,1508,1511],{"className":1507},[608],[574,1509],{"className":1510,"style":969},[612],[574,1512,1514,1517],{"className":1513},[617],[574,1515,891],{"className":1516},[617,618],[574,1518,1520],{"className":1519},[979],[574,1521,1523],{"className":1522},[670],[574,1524,1526],{"className":1525},[675],[574,1527,1529],{"className":1528,"style":969},[679],[574,1530,1531,1534],{"style":991},[574,1532],{"className":1533,"style":995},[687],[574,1535,1537],{"className":1536},[692,693,694,695],[574,1538,891],{"className":1539},[617,618,695],": Basis und Exponent sind variabel. Dafür braucht man die Ableitung von ",[574,1542,1544,1578],{"className":1543},[577],[574,1545,1547],{"className":1546},[581],[583,1548,1549],{"xmlns":585},[587,1550,1551,1575],{},[590,1552,1553,1556,1558,1560],{},[593,1554,1555],{},"f",[893,1557,1310],{"stretchy":1309},[593,1559,891],{},[951,1561,1562,1564],{},[893,1563,1321],{"stretchy":1309},[590,1565,1566,1569,1571,1573],{},[593,1567,1568],{},"g",[893,1570,1310],{"stretchy":1309},[593,1572,891],{},[893,1574,1321],{"stretchy":1309},[597,1576,1577],{"encoding":599},"f(x)^{g(x)}",[574,1579,1581],{"className":1580,"ariaHidden":604},[603],[574,1582,1584,1588,1592,1595,1598],{"className":1583},[608],[574,1585],{"className":1586,"style":1587},[612],"height:1.138em;vertical-align:-0.25em;",[574,1589,1555],{"className":1590,"style":1591},[617,618],"margin-right:0.1076em;",[574,1593,1310],{"className":1594},[662],[574,1596,891],{"className":1597},[617,618],[574,1599,1601,1604],{"className":1600},[745],[574,1602,1321],{"className":1603},[745],[574,1605,1607],{"className":1606},[979],[574,1608,1610],{"className":1609},[670],[574,1611,1613],{"className":1612},[675],[574,1614,1617],{"className":1615,"style":1616},[679],"height:0.888em;",[574,1618,1619,1622],{"style":991},[574,1620],{"className":1621,"style":995},[687],[574,1623,1625],{"className":1624},[692,693,694,695],[574,1626,1628,1631,1634,1637],{"className":1627},[617,695],[574,1629,1568],{"className":1630,"style":872},[617,618,695],[574,1632,1310],{"className":1633},[662,695],[574,1635,891],{"className":1636},[617,618,695],[574,1638,1321],{"className":1639},[745,695],[560,1641,1643],{"id":1642},"herleitung","Herleitung",[565,1645,1646,1647,1697],{},"Für ",[574,1648,1650,1667],{"className":1649},[577],[574,1651,1653],{"className":1652},[581],[583,1654,1655],{"xmlns":585},[587,1656,1657,1665],{},[590,1658,1659,1661,1663],{},[593,1660,891],{},[893,1662,895],{},[637,1664,898],{},[597,1666,901],{"encoding":599},[574,1668,1670,1688],{"className":1669,"ariaHidden":604},[603],[574,1671,1673,1676,1679,1682,1685],{"className":1672},[608],[574,1674],{"className":1675,"style":911},[612],[574,1677,891],{"className":1678},[617,618],[574,1680],{"className":1681,"style":919},[918],[574,1683,895],{"className":1684},[923],[574,1686],{"className":1687,"style":919},[918],[574,1689,1691,1694],{"className":1690},[608],[574,1692],{"className":1693,"style":933},[612],[574,1695,898],{"className":1696},[617]," schreibt man die Potenz mit der e-Funktion und leitet mit der Kettenregel ab:",[574,1699,1702],{"className":1700},[1701],"katex-display",[574,1703,1705,1825],{"className":1704},[577],[574,1706,1708],{"className":1707},[581],[583,1709,1711],{"xmlns":585,"display":1710},"block",[587,1712,1713,1822],{},[590,1714,1715,1721,1723,1738,1742,1745,1747,1749,1755,1761,1763,1777,1780,1786,1788,1794,1796,1802,1804,1806,1808],{},[951,1716,1717,1719],{},[593,1718,891],{},[593,1720,595],{},[893,1722,1143],{},[951,1724,1725,1728],{},[593,1726,1727],{},"e",[590,1729,1730,1732,1734,1736],{},[593,1731,595],{},[593,1733,1336],{},[893,1735,1339],{},[593,1737,891],{},[1739,1740,1741],"mtext",{},"  ",[893,1743,1744],{},"⇒",[1739,1746,1741],{},[893,1748,1310],{"stretchy":1309},[951,1750,1751,1753],{},[593,1752,891],{},[593,1754,595],{},[951,1756,1757,1759],{},[893,1758,1321],{"stretchy":1309},[893,1760,1325],{"mathvariant":1077,"lspace":1324,"rspace":1324},[893,1762,1143],{},[951,1764,1765,1767],{},[593,1766,1727],{},[590,1768,1769,1771,1773,1775],{},[593,1770,595],{},[593,1772,1336],{},[893,1774,1339],{},[593,1776,891],{},[893,1778,1779],{},"⋅",[634,1781,1782,1784],{},[593,1783,595],{},[593,1785,891],{},[893,1787,1143],{},[951,1789,1790,1792],{},[593,1791,891],{},[593,1793,595],{},[893,1795,1779],{},[634,1797,1798,1800],{},[593,1799,595],{},[593,1801,891],{},[893,1803,1143],{},[593,1805,595],{},[893,1807,1779],{},[951,1809,1810,1812],{},[593,1811,891],{},[590,1813,1814,1816,1819],{},[593,1815,595],{},[893,1817,1818],{},"−",[637,1820,1821],{},"1",[597,1823,1824],{"encoding":599},"x^r = e^{r \\ln x} \\;\\Rightarrow\\; (x^r)' = e^{r \\ln x} \\cdot \\frac{r}{x} = x^r \\cdot \\frac{r}{x} = r \\cdot x^{r-1}",[574,1826,1828,1874,1949,2030,2097,2179,2223,2300,2319],{"className":1827,"ariaHidden":604},[603],[574,1829,1831,1835,1865,1868,1871],{"className":1830},[608],[574,1832],{"className":1833,"style":1834},[612],"height:0.7144em;",[574,1836,1838,1841],{"className":1837},[617],[574,1839,891],{"className":1840},[617,618],[574,1842,1844],{"className":1843},[979],[574,1845,1847],{"className":1846},[670],[574,1848,1850],{"className":1849},[675],[574,1851,1853],{"className":1852,"style":1834},[679],[574,1854,1856,1859],{"style":1855},"top:-3.113em;margin-right:0.05em;",[574,1857],{"className":1858,"style":995},[687],[574,1860,1862],{"className":1861},[692,693,694,695],[574,1863,595],{"className":1864,"style":619},[617,618,695],[574,1866],{"className":1867,"style":919},[918],[574,1869,1143],{"className":1870},[923],[574,1872],{"className":1873,"style":919},[918],[574,1875,1877,1881,1934,1937,1940,1943,1946],{"className":1876},[608],[574,1878],{"className":1879,"style":1880},[612],"height:0.8991em;",[574,1882,1884,1887],{"className":1883},[617],[574,1885,1727],{"className":1886},[617,618],[574,1888,1890],{"className":1889},[979],[574,1891,1893],{"className":1892},[670],[574,1894,1896],{"className":1895},[675],[574,1897,1899],{"className":1898,"style":1880},[679],[574,1900,1901,1904],{"style":1855},[574,1902],{"className":1903,"style":995},[687],[574,1905,1907],{"className":1906},[692,693,694,695],[574,1908,1910,1913,1917,1928,1931],{"className":1909},[617,695],[574,1911,595],{"className":1912,"style":619},[617,618,695],[574,1914],{"className":1915,"style":1916},[918,695],"margin-right:0.1952em;",[574,1918,1920,1924],{"className":1919},[1472,695],[574,1921,1923],{"className":1922},[695],"l",[574,1925,1927],{"className":1926},[695],"n",[574,1929],{"className":1930,"style":1916},[918,695],[574,1932,891],{"className":1933},[617,618,695],[574,1935],{"className":1936,"style":919},[918],[574,1938],{"className":1939,"style":919},[918],[574,1941,1744],{"className":1942},[923],[574,1944],{"className":1945,"style":919},[918],[574,1947],{"className":1948,"style":919},[918],[574,1950,1952,1956,1959,1988,2021,2024,2027],{"className":1951},[608],[574,1953],{"className":1954,"style":1955},[612],"height:1.0519em;vertical-align:-0.25em;",[574,1957,1310],{"className":1958},[662],[574,1960,1962,1965],{"className":1961},[617],[574,1963,891],{"className":1964},[617,618],[574,1966,1968],{"className":1967},[979],[574,1969,1971],{"className":1970},[670],[574,1972,1974],{"className":1973},[675],[574,1975,1977],{"className":1976,"style":1834},[679],[574,1978,1979,1982],{"style":1855},[574,1980],{"className":1981,"style":995},[687],[574,1983,1985],{"className":1984},[692,693,694,695],[574,1986,595],{"className":1987,"style":619},[617,618,695],[574,1989,1991,1994],{"className":1990},[745],[574,1992,1321],{"className":1993},[745],[574,1995,1997],{"className":1996},[979],[574,1998,2000],{"className":1999},[670],[574,2001,2003],{"className":2002},[675],[574,2004,2007],{"className":2005,"style":2006},[679],"height:0.8019em;",[574,2008,2009,2012],{"style":1855},[574,2010],{"className":2011,"style":995},[687],[574,2013,2015],{"className":2014},[692,693,694,695],[574,2016,2018],{"className":2017},[617,695],[574,2019,1325],{"className":2020},[617,695],[574,2022],{"className":2023,"style":919},[918],[574,2025,1143],{"className":2026},[923],[574,2028],{"className":2029,"style":919},[918],[574,2031,2033,2036,2086,2090,2094],{"className":2032},[608],[574,2034],{"className":2035,"style":1880},[612],[574,2037,2039,2042],{"className":2038},[617],[574,2040,1727],{"className":2041},[617,618],[574,2043,2045],{"className":2044},[979],[574,2046,2048],{"className":2047},[670],[574,2049,2051],{"className":2050},[675],[574,2052,2054],{"className":2053,"style":1880},[679],[574,2055,2056,2059],{"style":1855},[574,2057],{"className":2058,"style":995},[687],[574,2060,2062],{"className":2061},[692,693,694,695],[574,2063,2065,2068,2071,2080,2083],{"className":2064},[617,695],[574,2066,595],{"className":2067,"style":619},[617,618,695],[574,2069],{"className":2070,"style":1916},[918,695],[574,2072,2074,2077],{"className":2073},[1472,695],[574,2075,1923],{"className":2076},[695],[574,2078,1927],{"className":2079},[695],[574,2081],{"className":2082,"style":1916},[918,695],[574,2084,891],{"className":2085},[617,618,695],[574,2087],{"className":2088,"style":2089},[918],"margin-right:0.2222em;",[574,2091,1779],{"className":2092},[2093],"mbin",[574,2095],{"className":2096,"style":2089},[918],[574,2098,2100,2104,2170,2173,2176],{"className":2099},[608],[574,2101],{"className":2102,"style":2103},[612],"height:1.7936em;vertical-align:-0.686em;",[574,2105,2107,2110,2167],{"className":2106},[617],[574,2108],{"className":2109},[662,663],[574,2111,2113],{"className":2112},[634],[574,2114,2116,2158],{"className":2115},[670,671],[574,2117,2119,2155],{"className":2118},[675],[574,2120,2123,2135,2143],{"className":2121,"style":2122},[679],"height:1.1076em;",[574,2124,2126,2129],{"style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Exponent:",[574,2372,2374],{"className":2373},[1701],[574,2375,2377,2447],{"className":2376},[577],[574,2378,2380],{"className":2379},[581],[583,2381,2382],{"xmlns":585,"display":1710},[587,2383,2384,2444],{},[590,2385,2386,2388,2390,2392,2394,2396,2404,2406,2408,2410,2416,2418,2420,2422,2424,2428,2430],{},[593,2387,1555],{},[893,2389,1310],{"stretchy":1309},[593,2391,891],{},[893,2393,1321],{"stretchy":1309},[893,2395,1143],{},[951,2397,2398,2400],{},[593,2399,891],{},[760,2401,2402],{},[637,2403,639],{},[1739,2405,1741],{},[893,2407,1744],{},[1739,2409,1741],{},[951,2411,2412,2414],{},[593,2413,1555],{},[893,2415,1325],{"mathvariant":1077,"lspace":1324,"rspace":1324},[893,2417,1310],{"stretchy":1309},[593,2419,891],{},[893,2421,1321],{"stretchy":1309},[893,2423,1143],{},[760,2425,2426],{},[637,2427,639],{},[893,2429,1779],{},[951,2431,2432,2434],{},[593,2433,891],{},[590,2435,2436,2440,2442],{},[760,2437,2438],{},[637,2439,639],{},[893,2441,1818],{},[637,2443,1821],{},[597,2445,2446],{"encoding":599},"f(x) = x^{\\sqrt{2}} \\;\\Rightarrow\\; f'(x) = \\sqrt{2} \\cdot x^{\\sqrt{2} - 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als Exponent:",[574,2793,2795],{"className":2794},[1701],[574,2796,2798,2891],{"className":2797},[577],[574,2799,2801],{"className":2800},[581],[583,2802,2803],{"xmlns":585,"display":1710},[587,2804,2805,2888],{},[590,2806,2807,2809,2811,2813,2815,2817,2824,2826,2828,2830,2836,2838,2840,2842,2844,2846,2848,2855,2858,2861,2867,2869,2872,2874,2876,2878,2880,2883,2885],{},[593,2808,1555],{},[893,2810,1310],{"stretchy":1309},[593,2812,891],{},[893,2814,1321],{"stretchy":1309},[893,2816,1143],{},[951,2818,2819,2821],{},[593,2820,891],{},[637,2822,2823],{},"2,5",[1739,2825,1741],{},[893,2827,1744],{},[1739,2829,1741],{},[951,2831,2832,2834],{},[593,2833,1555],{},[893,2835,1325],{"mathvariant":1077,"lspace":1324,"rspace":1324},[893,2837,1310],{"stretchy":1309},[593,2839,891],{},[893,2841,1321],{"stretchy":1309},[893,2843,1143],{},[637,2845,2823],{},[893,2847,1779],{},[951,2849,2850,2852],{},[593,2851,891],{},[637,2853,2854],{},"1,5",[893,2856,2857],{"separator":604},",",[918,2859],{"width":2860},"2em",[951,2862,2863,2865],{},[593,2864,1555],{},[893,2866,1325],{"mathvariant":1077,"lspace":1324,"rspace":1324},[893,2868,1310],{"stretchy":1309},[637,2870,2871],{},"4",[893,2873,1321],{"stretchy":1309},[893,2875,1143],{},[637,2877,2823],{},[893,2879,1779],{},[637,2881,2882],{},"8",[893,2884,1143],{},[637,2886,2887],{},"20",[597,2889,2890],{"encoding":599},"f(x) = x^{2{,}5} \\;\\Rightarrow\\; f'(x) = 2{,}5 \\cdot x^{1{,}5}, \\qquad f'(4) = 2{,}5 \\cdot 8 = 20",[574,2892,2894,2921,2985,3041,3069,3177,3204,3222],{"className":2893,"ariaHidden":604},[603],[574,2895,2897,2900,2903,2906,2909,2912,2915,2918],{"className":2896},[608],[574,2898],{"className":2899,"style":2456},[612],[574,2901,1555],{"className":2902,"style":1591},[617,618],[574,2904,1310],{"className":2905},[662],[574,2907,891],{"className":2908},[617,618],[574,2910,1321],{"className":2911},[745],[574,2913],{"className":2914,"style":919},[918],[574,2916,1143],{"className":2917},[923],[574,2919],{"className":2920,"style":919},[918],[574,2922,2924,2927,2970,2973,2976,2979,2982],{"className":2923},[608],[574,2925],{"className":2926,"style":2325},[612],[574,2928,2930,2933],{"className":2929},[617],[574,2931,891],{"className":2932},[617,618],[574,2934,2936],{"className":2935},[979],[574,2937,2939],{"className":2938},[670],[574,2940,2942],{"className":2941},[675],[574,2943,2945],{"className":2944,"style":2325},[679],[574,2946,2947,2950],{"style":1855},[574,2948],{"className":2949,"style":995},[687],[574,2951,2953],{"className":2952},[692,693,694,695],[574,2954,2956,2959,2966],{"className":2955},[617,695],[574,2957,639],{"className":2958},[617,695],[574,2960,2962],{"className":2961},[617,695],[574,2963,2857],{"className":2964},[2965,695],"mpunct",[574,2967,2969],{"className":2968},[617,695],"5",[574,2971],{"className":2972,"style":919},[918],[574,2974],{"className":2975,"style":919},[918],[574,2977,1744],{"className":2978},[923],[574,2980],{"className":2981,"style":919},[918],[574,2983],{"className":2984,"style":919},[918],[574,2986,2988,2991,3023,3026,3029,3032,3035,3038],{"className":2987},[608],[574,2989],{"className":2990,"style":1955},[612],[574,2992,2994,2997],{"className":2993},[617],[574,2995,1555],{"className":2996,"style":1591},[617,618],[574,2998,3000],{"className":2999},[979],[574,3001,3003],{"className":3002},[670],[574,3004,3006],{"className":3005},[675],[574,3007,3009],{"className":3008,"style":2006},[679],[574,3010,3011,3014],{"style":1855},[574,3012],{"className":3013,"style":995},[687],[574,3015,3017],{"className":3016},[692,693,694,695],[574,3018,3020],{"className":3019},[617,695],[574,3021,1325],{"className":3022},[617,695],[574,3024,1310],{"className":3025},[662],[574,3027,891],{"className":3028},[617,618],[574,3030,1321],{"className":3031},[745],[574,3033],{"className":3034,"style":919},[918],[574,3036,1143],{"className":3037},[923],[574,3039],{"className":3040,"style":919},[918],[574,3042,3044,3048,3051,3057,3060,3063,3066],{"className":3043},[608],[574,3045],{"className":3046,"style":3047},[612],"height:0.8389em;vertical-align:-0.1944em;",[574,3049,639],{"className":3050},[617],[574,3052,3054],{"className":3053},[617],[574,3055,2857],{"className":3056},[2965],[574,3058,2969],{"className":3059},[617],[574,3061],{"className":3062,"style":2089},[918],[574,3064,1779],{"className":3065},[2093],[574,3067],{"className":3068,"style":2089},[918],[574,3070,3072,3076,3117,3120,3124,3127,3159,3162,3165,3168,3171,3174],{"className":3071},[608],[574,3073],{"className":3074,"style":3075},[612],"height:1.1141em;vertical-align:-0.25em;",[574,3077,3079,3082],{"className":3078},[617],[574,3080,891],{"className":3081},[617,618],[574,3083,3085],{"className":3084},[979],[574,3086,3088],{"className":3087},[670],[574,3089,3091],{"className":3090},[675],[574,3092,3094],{"className":3093,"style":2325},[679],[574,3095,3096,3099],{"style":1855},[574,3097],{"className":3098,"style":995},[687],[574,3100,3102],{"className":3101},[692,693,694,695],[574,3103,3105,3108,3114],{"className":3104},[617,695],[574,3106,1821],{"className":3107},[617,695],[574,3109,3111],{"className":3110},[617,695],[574,3112,2857],{"className":3113},[2965,695],[574,3115,2969],{"className":3116},[617,695],[574,3118,2857],{"className":3119},[2965],[574,3121],{"className":3122,"style":3123},[918],"margin-right:2em;",[574,3125],{"className":3126,"style":1468},[918],[574,3128,3130,3133],{"className":3129},[617],[574,3131,1555],{"className":3132,"style":1591},[617,618],[574,3134,3136],{"className":3135},[979],[574,3137,3139],{"className":3138},[670],[574,3140,3142],{"className":3141},[675],[574,3143,3145],{"className":3144,"style":2006},[679],[574,3146,3147,3150],{"style":1855},[574,3148],{"className":3149,"style":995},[687],[574,3151,3153],{"className":3152},[692,693,694,695],[574,3154,3156],{"className":3155},[617,695],[574,3157,1325],{"className":3158},[617,695],[574,3160,1310],{"className":3161},[662],[574,3163,2871],{"className":3164},[617],[574,3166,1321],{"className":3167},[745],[574,3169],{"className":3170,"style":919},[918],[574,3172,1143],{"className":3173},[923],[574,3175],{"className":3176,"style":919},[918],[574,3178,3180,3183,3186,3192,3195,3198,3201],{"className":3179},[608],[574,3181],{"className":3182,"style":3047},[612],[574,3184,639],{"className":3185},[617],[574,3187,3189],{"className":3188},[617],[574,3190,2857],{"className":3191},[2965],[574,3193,2969],{"className":3194},[617],[574,3196],{"className":3197,"style":2089},[918],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im Nenner, vorher als Potenz geschrieben:",[574,3235,3237],{"className":3236},[1701],[574,3238,3240,3379],{"className":3239},[577],[574,3241,3243],{"className":3242},[581],[583,3244,3245],{"xmlns":585,"display":1710},[587,3246,3247,3376],{},[590,3248,3249,3251,3253,3255,3257,3259,3270,3272,3286,3288,3290,3292,3298,3300,3302,3304,3306,3308,3314,3316,3330,3332,3334,3340,3342,3344,3346,3348,3350,3356,3358,3365,3367,3369],{},[593,3250,1555],{},[893,3252,1310],{"stretchy":1309},[593,3254,891],{},[893,3256,1321],{"stretchy":1309},[893,3258,1143],{},[634,3260,3261,3263],{},[637,3262,1821],{},[3264,3265,3266,3268],"mroot",{},[593,3267,891],{},[637,3269,642],{},[893,3271,1143],{},[951,3273,3274,3276],{},[593,3275,891],{},[590,3277,3278,3280],{},[893,3279,1818],{},[634,3281,3282,3284],{},[637,3283,1821],{},[637,3285,642],{},[1739,3287,1741],{},[893,3289,1744],{},[1739,3291,1741],{},[951,3293,3294,3296],{},[593,3295,1555],{},[893,3297,1325],{"mathvariant":1077,"lspace":1324,"rspace":1324},[893,3299,1310],{"stretchy":1309},[593,3301,891],{},[893,3303,1321],{"stretchy":1309},[893,3305,1143],{},[893,3307,1818],{},[634,3309,3310,3312],{},[637,3311,1821],{},[637,3313,642],{},[893,3315,1779],{},[951,3317,3318,3320],{},[593,3319,891],{},[590,3321,3322,3324],{},[893,3323,1818],{},[634,3325,3326,3328],{},[637,3327,2871],{},[637,3329,642],{},[893,3331,2857],{"separator":604},[918,3333],{"width":2860},[951,3335,3336,3338],{},[593,3337,1555],{},[893,3339,1325],{"mathvariant":1077,"lspace":1324,"rspace":1324},[893,3341,1310],{"stretchy":1309},[637,3343,2882],{},[893,3345,1321],{"stretchy":1309},[893,3347,1143],{},[893,3349,1818],{},[634,3351,3352,3354],{},[637,3353,1821],{},[637,3355,642],{},[893,3357,1779],{},[634,3359,3360,3362],{},[637,3361,1821],{},[637,3363,3364],{},"16",[893,3366,1143],{},[893,3368,1818],{},[634,3370,3371,3373],{},[637,3372,1821],{},[637,3374,3375],{},"48",[597,3377,3378],{"encoding":599},"f(x) = \\frac{1}{\\sqrt[3]{x}} = x^{-\\frac{1}{3}} \\;\\Rightarrow\\; f'(x) = -\\frac{1}{3} \\cdot x^{-\\frac{4}{3}}, \\qquad f'(8) = -\\frac{1}{3} \\cdot \\frac{1}{16} = 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class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8833em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x > 0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","derivative-general-power","f(x) = x^r \\;\\Rightarrow\\; f'(x) = r \\cdot x^{r-1}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>r\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmo>⇒\u003C\u002Fmo>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmsup>\u003Cmi>f\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">′\u003C\u002Fmo>\u003C\u002Fmsup>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo 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encoding=\"application\u002Fx-tex\">f'(x)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0019em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7519em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">′\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan 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