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e^x",[568,1126,1128,1221],{"className":1127,"ariaHidden":598},[597],[568,1129,1131,1135,1138,1179,1212,1215,1218],{"className":1130},[602],[568,1132],{"className":1133,"style":1134},[606],"height:1.0019em;vertical-align:-0.25em;",[568,1136,641],{"className":1137},[667],[568,1139,1141,1144],{"className":1140},[611],[568,1142,980],{"className":1143},[611,612],[568,1145,1148],{"className":1146},[1147],"msupsub",[568,1149,1152],{"className":1150},[1151],"vlist-t",[568,1153,1156],{"className":1154},[1155],"vlist-r",[568,1157,1161],{"className":1158,"style":1160},[1159],"vlist","height:0.6644em;",[568,1162,1164,1169],{"style":1163},"top:-3.063em;margin-right:0.05em;",[568,1165],{"className":1166,"style":1168},[1167],"pstrut","height:2.7em;",[568,1170,1176],{"className":1171},[1172,1173,1174,1175],"sizing","reset-size6","size3","mtight",[568,1177,1104],{"className":1178},[611,612,1175],[568,1180,1182,1185],{"className":1181},[674],[568,1183,646],{"className":1184},[674],[568,1186,1188],{"className":1187},[1147],[568,1189,1191],{"className":1190},[1151],[568,1192,1194],{"className":1193},[1155],[568,1195,1198],{"className":1196,"style":1197},[1159],"height:0.7519em;",[568,1199,1200,1203],{"style":1163},[568,1201],{"className":1202,"style":1168},[1167],[568,1204,1206],{"className":1205},[1172,1173,1174,1175],[568,1207,1209],{"className":1208},[611,1175],[568,1210,1113],{"className":1211},[611,1175],[568,1213],{"className":1214,"style":724},[723],[568,1216,977],{"className":1217},[728],[568,1219],{"className":1220,"style":724},[723],[568,1222,1224,1227],{"className":1223},[602],[568,1225],{"className":1226,"style":1160},[606],[568,1228,1230,1233],{"className":1229},[611],[568,1231,980],{"className":1232},[611,612],[568,1234,1236],{"className":1235},[1147],[568,1237,1239],{"className":1238},[1151],[568,1240,1242],{"className":1241},[1155],[568,1243,1245],{"className":1244,"style":1160},[1159],[568,1246,1247,1250],{"style":1163},[568,1248],{"className":1249,"style":1168},[1167],[568,1251,1253],{"className":1252},[1172,1173,1174,1175],[568,1254,1104],{"className":1255},[611,612,1175],[559,1257,1259],{"id":1258},"herleitung","Herleitung",[564,1261,1262,1263,1414],{},"Jede Potenz mit positiver Basis lässt sich als e-Funktion schreiben: ",[568,1264,1266,1304],{"className":1265},[571],[568,1267,1269],{"className":1268},[575],[577,1270,1271],{"xmlns":579},[581,1272,1273,1301],{},[584,1274,1275,1281,1283],{},[1098,1276,1277,1279],{},[587,1278,589],{},[587,1280,1104],{},[635,1282,977],{},[1098,1284,1285,1287],{},[587,1286,980],{},[584,1288,1289,1291,1293,1295,1297,1299],{},[587,1290,1104],{},[587,1292,633],{},[635,1294,637],{},[635,1296,641],{"stretchy":640},[587,1298,589],{},[635,1300,646],{"stretchy":640},[591,1302,1303],{"encoding":593},"a^x = e^{x \\ln(a)}",[568,1305,1307,1351],{"className":1306,"ariaHidden":598},[597],[568,1308,1310,1313,1342,1345,1348],{"className":1309},[602],[568,1311],{"className":1312,"style":1160},[606],[568,1314,1316,1319],{"className":1315},[611],[568,1317,589],{"className":1318},[611,612],[568,1320,1322],{"className":1321},[1147],[568,1323,1325],{"className":1324},[1151],[568,1326,1328],{"className":1327},[1155],[568,1329,1331],{"className":1330,"style":1160},[1159],[568,1332,1333,1336],{"style":1163},[568,1334],{"className":1335,"style":1168},[1167],[568,1337,1339],{"className":1338},[1172,1173,1174,1175],[568,1340,1104],{"className":1341},[611,612,1175],[568,1343],{"className":1344,"style":724},[723],[568,1346,977],{"className":1347},[728],[568,1349],{"className":1350,"style":724},[723],[568,1352,1354,1358],{"className":1353},[602],[568,1355],{"className":1356,"style":1357},[606],"height:0.888em;",[568,1359,1361,1364],{"className":1360},[611],[568,1362,980],{"className":1363},[611,612],[568,1365,1367],{"className":1366},[1147],[568,1368,1370],{"className":1369},[1151],[568,1371,1373],{"className":1372},[1155],[568,1374,1376],{"className":1375,"style":1357},[1159],[568,1377,1378,1381],{"style":1163},[568,1379],{"className":1380,"style":1168},[1167],[568,1382,1384],{"className":1383},[1172,1173,1174,1175],[568,1385,1387,1390,1394,1405,1408,1411],{"className":1386},[611,1175],[568,1388,1104],{"className":1389},[611,612,1175],[568,1391],{"className":1392,"style":1393},[723,1175],"margin-right:0.1952em;",[568,1395,1397,1401],{"className":1396},[663,1175],[568,1398,1400],{"className":1399},[1175],"l",[568,1402,1404],{"className":1403},[1175],"n",[568,1406,641],{"className":1407},[667,1175],[568,1409,589],{"className":1410},[611,612,1175],[568,1412,646],{"className":1413},[674,1175],". Mit der Kettenregel folgt",[568,1416,1419],{"className":1417},[1418],"katex-display",[568,1420,1422,1516],{"className":1421},[571],[568,1423,1425],{"className":1424},[575],[577,1426,1428],{"xmlns":579,"display":1427},"block",[581,1429,1430,1513],{},[584,1431,1432,1460,1462,1480,1483,1485,1487,1489,1491,1493,1495,1497,1499,1501,1503,1505,1507],{},[1098,1433,1434,1458],{},[584,1435,1436,1438,1456],{},[635,1437,641],{"fence":598},[1098,1439,1440,1442],{},[587,1441,980],{},[584,1443,1444,1446,1448,1450,1452,1454],{},[587,1445,1104],{},[587,1447,633],{},[635,1449,637],{},[635,1451,641],{"stretchy":640},[587,1453,589],{},[635,1455,646],{"stretchy":640},[635,1457,646],{"fence":598},[635,1459,1113],{"mathvariant":1111,"lspace":1112,"rspace":1112},[635,1461,977],{},[1098,1463,1464,1466],{},[587,1465,980],{},[584,1467,1468,1470,1472,1474,1476,1478],{},[587,1469,1104],{},[587,1471,633],{},[635,1473,637],{},[635,1475,641],{"stretchy":640},[587,1477,589],{},[635,1479,646],{"stretchy":640},[635,1481,1482],{},"⋅",[587,1484,633],{},[635,1486,637],{},[635,1488,641],{"stretchy":640},[587,1490,589],{},[635,1492,646],{"stretchy":640},[635,1494,977],{},[587,1496,633],{},[635,1498,637],{},[635,1500,641],{"stretchy":640},[587,1502,589],{},[635,1504,646],{"stretchy":640},[635,1506,1482],{},[1098,1508,1509,1511],{},[587,1510,589],{},[587,1512,1104],{},[591,1514,1515],{"encoding":593},"\\left(e^{x \\ln(a)}\\right)' = e^{x \\ln(a)} \\cdot \\ln(a) = \\ln(a) \\cdot a^x",[568,1517,1519,1641,1711,1738,1765],{"className":1518,"ariaHidden":598},[597],[568,1520,1522,1526,1632,1635,1638],{"className":1521},[602],[568,1523],{"className":1524,"style":1525},[606],"height:1.9418em;vertical-align:-0.65em;",[568,1527,1530,1604],{"className":1528},[1529],"minner",[568,1531,1533,1543,1598],{"className":1532},[1529],[568,1534,1538],{"className":1535,"style":1537},[667,1536],"delimcenter","top:0em;",[568,1539,641],{"className":1540},[1541,1542],"delimsizing","size2",[568,1544,1546,1549],{"className":1545},[611],[568,1547,980],{"className":1548},[611,612],[568,1550,1552],{"className":1551},[1147],[568,1553,1555],{"className":1554},[1151],[568,1556,1558],{"className":1557},[1155],[568,1559,1562],{"className":1560,"style":1561},[1159],"height:0.938em;",[568,1563,1565,1568],{"style":1564},"top:-3.113em;margin-right:0.05em;",[568,1566],{"className":1567,"style":1168},[1167],[568,1569,1571],{"className":1570},[1172,1173,1174,1175],[568,1572,1574,1577,1580,1589,1592,1595],{"className":1573},[611,1175],[568,1575,1104],{"className":1576},[611,612,1175],[568,1578],{"className":1579,"style":1393},[723,1175],[568,1581,1583,1586],{"className":1582},[663,1175],[568,1584,1400],{"className":1585},[1175],[568,1587,1404],{"className":1588},[1175],[568,1590,641],{"className":1591},[667,1175],[568,1593,589],{"className":1594},[611,612,1175],[568,1596,646],{"className":1597},[674,1175],[568,1599,1601],{"className":1600,"style":1537},[674,1536],[568,1602,646],{"className":1603},[1541,1542],[568,1605,1607],{"className":1606},[1147],[568,1608,1610],{"className":1609},[1151],[568,1611,1613],{"className":1612},[1155],[568,1614,1617],{"className":1615,"style":1616},[1159],"height:1.2918em;",[568,1618,1620,1623],{"style":1619},"top:-3.6029em;margin-right:0.05em;",[568,1621],{"className":1622,"style":1168},[1167],[568,1624,1626],{"className":1625},[1172,1173,1174,1175],[568,1627,1629],{"className":1628},[611,1175],[568,1630,1113],{"className":1631},[611,1175],[568,1633],{"className":1634,"style":724},[723],[568,1636,977],{"className":1637},[728],[568,1639],{"className":1640,"style":724},[723],[568,1642,1644,1647,1700,1704,1708],{"className":1643},[602],[568,1645],{"className":1646,"style":1561},[606],[568,1648,1650,1653],{"className":1649},[611],[568,1651,980],{"className":1652},[611,612],[568,1654,1656],{"className":1655},[1147],[568,1657,1659],{"className":1658},[1151],[568,1660,1662],{"className":1661},[1155],[568,1663,1665],{"className":1664,"style":1561},[1159],[568,1666,1667,1670],{"style":1564},[568,1668],{"className":1669,"style":1168},[1167],[568,1671,1673],{"className":1672},[1172,1173,1174,1175],[568,1674,1676,1679,1682,1691,1694,1697],{"className":1675},[611,1175],[568,1677,1104],{"className":1678},[611,612,1175],[568,1680],{"className":1681,"style":1393},[723,1175],[568,1683,1685,1688],{"className":1684},[663,1175],[568,1686,1400],{"className":1687},[1175],[568,1689,1404],{"className":1690},[1175],[568,1692,641],{"className":1693},[667,1175],[568,1695,589],{"className":1696},[611,612,1175],[568,1698,646],{"className":1699},[674,1175],[568,1701],{"className":1702,"style":1703},[723],"margin-right:0.2222em;",[568,1705,1482],{"className":1706},[1707],"mbin",[568,1709],{"className":1710,"style":1703},[723],[568,1712,1714,1717,1720,1723,1726,1729,1732,1735],{"className":1713},[602],[568,1715],{"className":1716,"style":659},[606],[568,1718,633],{"className":1719},[663],[568,1721,641],{"className":1722},[667],[568,1724,589],{"className":1725},[611,612],[568,1727,646],{"className":1728},[674],[568,1730],{"className":1731,"style":724},[723],[568,1733,977],{"className":1734},[728],[568,1736],{"className":1737,"style":724},[723],[568,1739,1741,1744,1747,1750,1753,1756,1759,1762],{"className":1740},[602],[568,1742],{"className":1743,"style":659},[606],[568,1745,633],{"className":1746},[663],[568,1748,641],{"className":1749},[667],[568,1751,589],{"className":1752},[611,612],[568,1754,646],{"className":1755},[674],[568,1757],{"className":1758,"style":1703},[723],[568,1760,1482],{"className":1761},[1707],[568,1763],{"className":1764,"style":1703},[723],[568,1766,1768,1772],{"className":1767},[602],[568,1769],{"className":1770,"style":1771},[606],"height:0.7144em;",[568,1773,1775,1778],{"className":1774},[611],[568,1776,589],{"className":1777},[611,612],[568,1779,1781],{"className":1780},[1147],[568,1782,1784],{"className":1783},[1151],[568,1785,1787],{"className":1786},[1155],[568,1788,1790],{"className":1789,"style":1771},[1159],[568,1791,1792,1795],{"style":1564},[568,1793],{"className":1794,"style":1168},[1167],[568,1796,1798],{"className":1797},[1172,1173,1174,1175],[568,1799,1104],{"className":1800},[611,612,1175],[559,1802,1804],{"id":1803},"beispiele","Beispiele",[568,1806,1808],{"className":1807},[1418],[568,1809,1811,1922],{"className":1810},[571],[568,1812,1814],{"className":1813},[575],[577,1815,1816],{"xmlns":579,"display":1427},[581,1817,1818,1919],{},[584,1819,1820,1823,1825,1827,1829,1831,1838,1842,1845,1847,1853,1855,1857,1859,1861,1863,1865,1867,1869,1871,1873,1879,1882,1885,1891,1893,1896,1898,1900,1903,1905,1907,1909,1911,1913,1916],{},[587,1821,1822],{},"f",[635,1824,641],{"stretchy":640},[587,1826,1104],{},[635,1828,646],{"stretchy":640},[635,1830,977],{},[1098,1832,1833,1836],{},[701,1834,1835],{},"2",[587,1837,1104],{},[1839,1840,1841],"mtext",{},"  ",[635,1843,1844],{},"⇒",[1839,1846,1841],{},[1098,1848,1849,1851],{},[587,1850,1822],{},[635,1852,1113],{"mathvariant":1111,"lspace":1112,"rspace":1112},[635,1854,641],{"stretchy":640},[587,1856,1104],{},[635,1858,646],{"stretchy":640},[635,1860,977],{},[587,1862,633],{},[635,1864,637],{},[635,1866,641],{"stretchy":640},[701,1868,1835],{},[635,1870,646],{"stretchy":640},[635,1872,1482],{},[1098,1874,1875,1877],{},[701,1876,1835],{},[587,1878,1104],{},[635,1880,1881],{"separator":598},",",[723,1883],{"width":1884},"1em",[1098,1886,1887,1889],{},[587,1888,1822],{},[635,1890,1113],{"mathvariant":1111,"lspace":1112,"rspace":1112},[635,1892,641],{"stretchy":640},[701,1894,1895],{},"3",[635,1897,646],{"stretchy":640},[635,1899,977],{},[701,1901,1902],{},"8",[587,1904,633],{},[635,1906,637],{},[635,1908,641],{"stretchy":640},[701,1910,1835],{},[635,1912,646],{"stretchy":640},[635,1914,1915],{},"≈",[701,1917,1918],{},"5,545",[591,1920,1921],{"encoding":593},"f(x) = 2^x \\;\\Rightarrow\\; f'(x) = \\ln(2) \\cdot 2^x, \\quad f'(3) = 8 \\ln(2) \\approx 5{,}545",[568,1923,1925,1953,2003,2061,2088,2185,2218],{"className":1924,"ariaHidden":598},[597],[568,1926,1928,1931,1935,1938,1941,1944,1947,1950],{"className":1927},[602],[568,1929],{"className":1930,"style":659},[606],[568,1932,1822],{"className":1933,"style":1934},[611,612],"margin-right:0.1076em;",[568,1936,641],{"className":1937},[667],[568,1939,1104],{"className":1940},[611,612],[568,1942,646],{"className":1943},[674],[568,1945],{"className":1946,"style":724},[723],[568,1948,977],{"className":1949},[728],[568,1951],{"className":1952,"style":724},[723],[568,1954,1956,1959,1988,1991,1994,1997,2000],{"className":1955},[602],[568,1957],{"className":1958,"style":1771},[606],[568,1960,1962,1965],{"className":1961},[611],[568,1963,1835],{"className":1964},[611],[568,1966,1968],{"className":1967},[1147],[568,1969,1971],{"className":1970},[1151],[568,1972,1974],{"className":1973},[1155],[568,1975,1977],{"className":1976,"style":1771},[1159],[568,1978,1979,1982],{"style":1564},[568,1980],{"className":1981,"style":1168},[1167],[568,1983,1985],{"className":1984},[1172,1173,1174,1175],[568,1986,1104],{"className":1987},[611,612,1175],[568,1989],{"className":1990,"style":724},[723],[568,1992],{"className":1993,"style":724},[723],[568,1995,1844],{"className":1996},[728],[568,1998],{"className":1999,"style":724},[723],[568,2001],{"className":2002,"style":724},[723],[568,2004,2006,2010,2043,2046,2049,2052,2055,2058],{"className":2005},[602],[568,2007],{"className":2008,"style":2009},[606],"height:1.0519em;vertical-align:-0.25em;",[568,2011,2013,2016],{"className":2012},[611],[568,2014,1822],{"className":2015,"style":1934},[611,612],[568,2017,2019],{"className":2018},[1147],[568,2020,2022],{"className":2021},[1151],[568,2023,2025],{"className":2024},[1155],[568,2026,2029],{"className":2027,"style":2028},[1159],"height:0.8019em;",[568,2030,2031,2034],{"style":1564},[568,2032],{"className":2033,"style":1168},[1167],[568,2035,2037],{"className":2036},[1172,1173,1174,1175],[568,2038,2040],{"className":2039},[611,1175],[568,2041,1113],{"className":2042},[611,1175],[568,2044,641],{"className":2045},[667],[568,2047,1104],{"className":2048},[611,612],[568,2050,646],{"className":2051},[674],[568,2053],{"className":2054,"style":724},[723],[568,2056,977],{"className":2057},[728],[568,2059],{"className":2060,"style":724},[723],[568,2062,2064,2067,2070,2073,2076,2079,2082,2085],{"className":2063},[602],[568,2065],{"className":2066,"style":659},[606],[568,2068,633],{"className":2069},[663],[568,2071,641],{"className":2072},[667],[568,2074,1835],{"className":2075},[611],[568,2077,646],{"className":2078},[674],[568,2080],{"className":2081,"style":1703},[723],[568,2083,1482],{"className":2084},[1707],[568,2086],{"className":2087,"style":1703},[723],[568,2089,2091,2094,2123,2127,2131,2135,2167,2170,2173,2176,2179,2182],{"className":2090},[602],[568,2092],{"className":2093,"style":2009},[606],[568,2095,2097,2100],{"className":2096},[611],[568,2098,1835],{"className":2099},[611],[568,2101,2103],{"className":2102},[1147],[568,2104,2106],{"className":2105},[1151],[568,2107,2109],{"className":2108},[1155],[568,2110,2112],{"className":2111,"style":1771},[1159],[568,2113,2114,2117],{"style":1564},[568,2115],{"className":2116,"style":1168},[1167],[568,2118,2120],{"className":2119},[1172,1173,1174,1175],[568,2121,1104],{"className":2122},[611,612,1175],[568,2124,1881],{"className":2125},[2126],"mpunct",[568,2128],{"className":2129,"style":2130},[723],"margin-right:1em;",[568,2132],{"className":2133,"style":2134},[723],"margin-right:0.1667em;",[568,2136,2138,2141],{"className":2137},[611],[568,2139,1822],{"className":2140,"style":1934},[611,612],[568,2142,2144],{"className":2143},[1147],[568,2145,2147],{"className":2146},[1151],[568,2148,2150],{"className":2149},[1155],[568,2151,2153],{"className":2152,"style":2028},[1159],[568,2154,2155,2158],{"style":1564},[568,2156],{"className":2157,"style":1168},[1167],[568,2159,2161],{"className":2160},[1172,1173,1174,1175],[568,2162,2164],{"className":2163},[611,1175],[568,2165,1113],{"className":2166},[611,1175],[568,2168,641],{"className":2169},[667],[568,2171,1895],{"className":2172},[611],[568,2174,646],{"className":2175},[674],[568,2177],{"className":2178,"style":724},[723],[568,2180,977],{"className":2181},[728],[568,2183],{"className":2184,"style":724},[723],[568,2186,2188,2191,2194,2197,2200,2203,2206,2209,2212,2215],{"className":2187},[602],[568,2189],{"className":2190,"style":659},[606],[568,2192,1902],{"className":2193},[611],[568,2195],{"className":2196,"style":2134},[723],[568,2198,633],{"className":2199},[663],[568,2201,641],{"className":2202},[667],[568,2204,1835],{"className":2205},[611],[568,2207,646],{"className":2208},[674],[568,2210],{"className":2211,"style":724},[723],[568,2213,1915],{"className":2214},[728],[568,2216],{"className":2217,"style":724},[723],[568,2219,2221,2225,2229,2235],{"className":2220},[602],[568,2222],{"className":2223,"style":2224},[606],"height:0.8389em;vertical-align:-0.1944em;",[568,2226,2228],{"className":2227},[611],"5",[568,2230,2232],{"className":2231},[611],[568,2233,1881],{"className":2234},[2126],[568,2236,2238],{"className":2237},[611],"545",[568,2240,2242],{"className":2241},[1418],[568,2243,2245,2328],{"className":2244},[571],[568,2246,2248],{"className":2247},[575],[577,2249,2250],{"xmlns":579,"display":1427},[581,2251,2252,2325],{},[584,2253,2254,2256,2258,2260,2262,2264,2271,2273,2275,2277,2283,2285,2287,2289,2291,2293,2295,2297,2299,2301,2303,2309,2311,2314,2317,2319],{},[587,2255,1822],{},[635,2257,641],{"stretchy":640},[587,2259,1104],{},[635,2261,646],{"stretchy":640},[635,2263,977],{},[1098,2265,2266,2269],{},[701,2267,2268],{},"0,5",[587,2270,1104],{},[1839,2272,1841],{},[635,2274,1844],{},[1839,2276,1841],{},[1098,2278,2279,2281],{},[587,2280,1822],{},[635,2282,1113],{"mathvariant":1111,"lspace":1112,"rspace":1112},[635,2284,641],{"stretchy":640},[587,2286,1104],{},[635,2288,646],{"stretchy":640},[635,2290,977],{},[587,2292,633],{},[635,2294,637],{},[635,2296,641],{"stretchy":640},[701,2298,2268],{},[635,2300,646],{"stretchy":640},[635,2302,1482],{},[1098,2304,2305,2307],{},[701,2306,2268],{},[587,2308,1104],{},[635,2310,1915],{},[635,2312,2313],{},"−",[701,2315,2316],{},"0,6931",[635,2318,1482],{},[1098,2320,2321,2323],{},[701,2322,2268],{},[587,2324,1104],{},[591,2326,2327],{"encoding":593},"f(x) = 0{,}5^x \\;\\Rightarrow\\; f'(x) = \\ln(0{,}5) \\cdot 0{,}5^x \\approx -0{,}6931 \\cdot 0{,}5^x",[568,2329,2331,2358,2418,2474,2510,2563,2594],{"className":2330,"ariaHidden":598},[597],[568,2332,2334,2337,2340,2343,2346,2349,2352,2355],{"className":2333},[602],[568,2335],{"className":2336,"style":659},[606],[568,2338,1822],{"className":2339,"style":1934},[611,612],[568,2341,641],{"className":2342},[667],[568,2344,1104],{"className":2345},[611,612],[568,2347,646],{"className":2348},[674],[568,2350],{"className":2351,"style":724},[723],[568,2353,977],{"className":2354},[728],[568,2356],{"className":2357,"style":724},[723],[568,2359,2361,2365,2368,2374,2403,2406,2409,2412,2415],{"className":2360},[602],[568,2362],{"className":2363,"style":2364},[606],"height:0.9088em;vertical-align:-0.1944em;",[568,2366,769],{"className":2367},[611],[568,2369,2371],{"className":2370},[611],[568,2372,1881],{"className":2373},[2126],[568,2375,2377,2380],{"className":2376},[611],[568,2378,2228],{"className":2379},[611],[568,2381,2383],{"className":2382},[1147],[568,2384,2386],{"className":2385},[1151],[568,2387,2389],{"className":2388},[1155],[568,2390,2392],{"className":2391,"style":1771},[1159],[568,2393,2394,2397],{"style":1564},[568,2395],{"className":2396,"style":1168},[1167],[568,2398,2400],{"className":2399},[1172,1173,1174,1175],[568,2401,1104],{"className":2402},[611,612,1175],[568,2404],{"className":2405,"style":724},[723],[568,2407],{"className":2408,"style":724},[723],[568,2410,1844],{"className":2411},[728],[568,2413],{"className":2414,"style":724},[723],[568,2416],{"className":2417,"style":724},[723],[568,2419,2421,2424,2456,2459,2462,2465,2468,2471],{"className":2420},[602],[568,2422],{"className":2423,"style":2009},[606],[568,2425,2427,2430],{"className":2426},[611],[568,2428,1822],{"className":2429,"style":1934},[611,612],[568,2431,2433],{"className":2432},[1147],[568,2434,2436],{"className":2435},[1151],[568,2437,2439],{"className":2438},[1155],[568,2440,2442],{"className":2441,"style":2028},[1159],[568,2443,2444,2447],{"style":1564},[568,2445],{"className":2446,"style":1168},[1167],[568,2448,2450],{"className":2449},[1172,1173,1174,1175],[568,2451,2453],{"className":2452},[611,1175],[568,2454,1113],{"className":2455},[611,1175],[568,2457,641],{"className":2458},[667],[568,2460,1104],{"className":2461},[611,612],[568,2463,646],{"className":2464},[674],[568,2466],{"className":2467,"style":724},[723],[568,2469,977],{"className":2470},[728],[568,2472],{"className":2473,"style":724},[723],[568,2475,2477,2480,2483,2486,2489,2495,2498,2501,2504,2507],{"className":2476},[602],[568,2478],{"className":2479,"style":659},[606],[568,2481,633],{"className":2482},[663],[568,2484,641],{"className":2485},[667],[568,2487,769],{"className":2488},[611],[568,2490,2492],{"className":2491},[611],[568,2493,1881],{"className":2494},[2126],[568,2496,2228],{"className":2497},[611],[568,2499,646],{"className":2500},[674],[568,2502],{"className":2503,"style":1703},[723],[568,2505,1482],{"className":2506},[1707],[568,2508],{"className":2509,"style":1703},[723],[568,2511,2513,2516,2519,2525,2554,2557,2560],{"className":2512},[602],[568,2514],{"className":2515,"style":2364},[606],[568,2517,769],{"className":2518},[611],[568,2520,2522],{"className":2521},[611],[568,2523,1881],{"className":2524},[2126],[568,2526,2528,2531],{"className":2527},[611],[568,2529,2228],{"className":2530},[611],[568,2532,2534],{"className":2533},[1147],[568,2535,2537],{"className":2536},[1151],[568,2538,2540],{"className":2539},[1155],[568,2541,2543],{"className":2542,"style":1771},[1159],[568,2544,2545,2548],{"style":1564},[568,2546],{"className":2547,"style":1168},[1167],[568,2549,2551],{"className":2550},[1172,1173,1174,1175],[568,2552,1104],{"className":2553},[611,612,1175],[568,2555],{"className":2556,"style":724},[723],[568,2558,1915],{"className":2559},[728],[568,2561],{"className":2562,"style":724},[723],[568,2564,2566,2569,2572,2575,2581,2585,2588,2591],{"className":2565},[602],[568,2567],{"className":2568,"style":2224},[606],[568,2570,2313],{"className":2571},[611],[568,2573,769],{"className":2574},[611],[568,2576,2578],{"className":2577},[611],[568,2579,1881],{"className":2580},[2126],[568,2582,2584],{"className":2583},[611],"6931",[568,2586],{"className":2587,"style":1703},[723],[568,2589,1482],{"className":2590},[1707],[568,2592],{"className":2593,"style":1703},[723],[568,2595,2597,2600,2603,2609],{"className":2596},[602],[568,2598],{"className":2599,"style":2364},[606],[568,2601,769],{"className":2602},[611],[568,2604,2606],{"className":2605},[611],[568,2607,1881],{"className":2608},[2126],[568,2610,2612,2615],{"className":2611},[611],[568,2613,2228],{"className":2614},[611],[568,2616,2618],{"className":2617},[1147],[568,2619,2621],{"className":2620},[1151],[568,2622,2624],{"className":2623},[1155],[568,2625,2627],{"className":2626,"style":1771},[1159],[568,2628,2629,2632],{"style":1564},[568,2630],{"className":2631,"style":1168},[1167],[568,2633,2635],{"className":2634},[1172,1173,1174,1175],[568,2636,1104],{"className":2637},[611,612,1175],[564,2639,2640,2641,2778,2779,2808],{},"Eine Bakterienkultur wächst nach ",[568,2642,2644,2680],{"className":2643},[571],[568,2645,2647],{"className":2646},[575],[577,2648,2649],{"xmlns":579},[581,2650,2651,2677],{},[584,2652,2653,2656,2658,2661,2663,2665,2668,2670],{},[587,2654,2655],{},"N",[635,2657,641],{"stretchy":640},[587,2659,2660],{},"t",[635,2662,646],{"stretchy":640},[635,2664,977],{},[701,2666,2667],{},"100",[635,2669,1482],{},[1098,2671,2672,2675],{},[701,2673,2674],{},"1,05",[587,2676,2660],{},[591,2678,2679],{"encoding":593},"N(t) = 100 \\cdot 1{,}05^t",[568,2681,2683,2711,2729],{"className":2682,"ariaHidden":598},[597],[568,2684,2686,2689,2693,2696,2699,2702,2705,2708],{"className":2685},[602],[568,2687],{"className":2688,"style":659},[606],[568,2690,2655],{"className":2691,"style":2692},[611,612],"margin-right:0.109em;",[568,2694,641],{"className":2695},[667],[568,2697,2660],{"className":2698},[611,612],[568,2700,646],{"className":2701},[674],[568,2703],{"className":2704,"style":724},[723],[568,2706,977],{"className":2707},[728],[568,2709],{"className":2710,"style":724},[723],[568,2712,2714,2717,2720,2723,2726],{"className":2713},[602],[568,2715],{"className":2716,"style":738},[606],[568,2718,2667],{"className":2719},[611],[568,2721],{"className":2722,"style":1703},[723],[568,2724,1482],{"className":2725},[1707],[568,2727],{"className":2728,"style":1703},[723],[568,2730,2732,2736,2739,2745,2748],{"className":2731},[602],[568,2733],{"className":2734,"style":2735},[606],"height:0.988em;vertical-align:-0.1944em;",[568,2737,703],{"className":2738},[611],[568,2740,2742],{"className":2741},[611],[568,2743,1881],{"className":2744},[2126],[568,2746,769],{"className":2747},[611],[568,2749,2751,2754],{"className":2750},[611],[568,2752,2228],{"className":2753},[611],[568,2755,2757],{"className":2756},[1147],[568,2758,2760],{"className":2759},[1151],[568,2761,2763],{"className":2762},[1155],[568,2764,2767],{"className":2765,"style":2766},[1159],"height:0.7936em;",[568,2768,2769,2772],{"style":1163},[568,2770],{"className":2771,"style":1168},[1167],[568,2773,2775],{"className":2774},[1172,1173,1174,1175],[568,2776,2660],{"className":2777},[611,612,1175]," (",[568,2780,2782,2795],{"className":2781},[571],[568,2783,2785],{"className":2784},[575],[577,2786,2787],{"xmlns":579},[581,2788,2789,2793],{},[584,2790,2791],{},[587,2792,2660],{},[591,2794,2660],{"encoding":593},[568,2796,2798],{"className":2797,"ariaHidden":598},[597],[568,2799,2801,2805],{"className":2800},[602],[568,2802],{"className":2803,"style":2804},[606],"height:0.6151em;",[568,2806,2660],{"className":2807},[611,612]," in Stunden). Die momentane Wachstumsgeschwindigkeit zu Beginn ist",[568,2810,2812],{"className":2811},[1418],[568,2813,2815,2871],{"className":2814},[571],[568,2816,2818],{"className":2817},[575],[577,2819,2820],{"xmlns":579,"display":1427},[581,2821,2822,2868],{},[584,2823,2824,2830,2832,2834,2836,2838,2840,2842,2844,2846,2848,2850,2852,2854,2860,2862,2865],{},[1098,2825,2826,2828],{},[587,2827,2655],{},[635,2829,1113],{"mathvariant":1111,"lspace":1112,"rspace":1112},[635,2831,641],{"stretchy":640},[701,2833,769],{},[635,2835,646],{"stretchy":640},[635,2837,977],{},[701,2839,2667],{},[635,2841,1482],{},[587,2843,633],{},[635,2845,637],{},[635,2847,641],{"stretchy":640},[701,2849,2674],{},[635,2851,646],{"stretchy":640},[635,2853,1482],{},[1098,2855,2856,2858],{},[701,2857,2674],{},[701,2859,769],{},[635,2861,1915],{},[701,2863,2864],{},"4,88",[1839,2866,2867],{}," Bakterien pro Stunde",[591,2869,2870],{"encoding":593},"N'(0) = 100 \\cdot \\ln(1{,}05) \\cdot 1{,}05^0 \\approx 4{,}88 \\text{ Bakterien pro Stunde}",[568,2872,2874,2930,2948,2985,3043],{"className":2873,"ariaHidden":598},[597],[568,2875,2877,2880,2912,2915,2918,2921,2924,2927],{"className":2876},[602],[568,2878],{"className":2879,"style":2009},[606],[568,2881,2883,2886],{"className":2882},[611],[568,2884,2655],{"className":2885,"style":2692},[611,612],[568,2887,2889],{"className":2888},[1147],[568,2890,2892],{"className":2891},[1151],[568,2893,2895],{"className":2894},[1155],[568,2896,2898],{"className":2897,"style":2028},[1159],[568,2899,2900,2903],{"style":1564},[568,2901],{"className":2902,"style":1168},[1167],[568,2904,2906],{"className":2905},[1172,1173,1174,1175],[568,2907,2909],{"className":2908},[611,1175],[568,2910,1113],{"className":2911},[611,1175],[568,2913,641],{"className":2914},[667],[568,2916,769],{"className":2917},[611],[568,2919,646],{"className":2920},[674],[568,2922],{"className":2923,"style":724},[723],[568,2925,977],{"className":2926},[728],[568,2928],{"className":2929,"style":724},[723],[568,2931,2933,2936,2939,2942,2945],{"className":2932},[602],[568,2934],{"className":2935,"style":738},[606],[568,2937,2667],{"className":2938},[611],[568,2940],{"className":2941,"style":1703},[723],[568,2943,1482],{"className":2944},[1707],[568,2946],{"className":2947,"style":1703},[723],[568,2949,2951,2954,2957,2960,2963,2969,2973,2976,2979,2982],{"className":2950},[602],[568,2952],{"className":2953,"style":659},[606],[568,2955,633],{"className":2956},[663],[568,2958,641],{"className":2959},[667],[568,2961,703],{"className":2962},[611],[568,2964,2966],{"className":2965},[611],[568,2967,1881],{"className":2968},[2126],[568,2970,2972],{"className":2971},[611],"05",[568,2974,646],{"className":2975},[674],[568,2977],{"className":2978,"style":1703},[723],[568,2980,1482],{"className":2981},[1707],[568,2983],{"className":2984,"style":1703},[723],[568,2986,2988,2992,2995,3001,3004,3034,3037,3040],{"className":2987},[602],[568,2989],{"className":2990,"style":2991},[606],"height:1.0585em;vertical-align:-0.1944em;",[568,2993,703],{"className":2994},[611],[568,2996,2998],{"className":2997},[611],[568,2999,1881],{"className":3000},[2126],[568,3002,769],{"className":3003},[611],[568,3005,3007,3010],{"className":3006},[611],[568,3008,2228],{"className":3009},[611],[568,3011,3013],{"className":3012},[1147],[568,3014,3016],{"className":3015},[1151],[568,3017,3019],{"className":3018},[1155],[568,3020,3023],{"className":3021,"style":3022},[1159],"height:0.8641em;",[568,3024,3025,3028],{"style":1564},[568,3026],{"className":3027,"style":1168},[1167],[568,3029,3031],{"className":3030},[1172,1173,1174,1175],[568,3032,769],{"className":3033},[611,1175],[568,3035],{"className":3036,"style":724},[723],[568,3038,1915],{"className":3039},[728],[568,3041],{"className":3042,"style":724},[723],[568,3044,3046,3050,3054,3060,3064],{"className":3045},[602],[568,3047],{"className":3048,"style":3049},[606],"height:0.8889em;vertical-align:-0.1944em;",[568,3051,3053],{"className":3052},[611],"4",[568,3055,3057],{"className":3056},[611],[568,3058,1881],{"className":3059},[2126],[568,3061,3063],{"className":3062},[611],"88",[568,3065,3068],{"className":3066},[611,3067],"text",[568,3069,2867],{"className":3070},[611],[559,3072,3074],{"id":3073},"typische-fehler","Typische Fehler",[677,3076,3077,3274,3506],{},[680,3078,3079,3080,3273],{},"Die Potenzregel anwenden: ",[568,3081,3083,3127],{"className":3082},[571],[568,3084,3086],{"className":3085},[575],[577,3087,3088],{"xmlns":579},[581,3089,3090,3124],{},[584,3091,3092,3094,3100,3106,3108,3110,3112],{},[635,3093,641],{"stretchy":640},[1098,3095,3096,3098],{},[701,3097,1835],{},[587,3099,1104],{},[1098,3101,3102,3104],{},[635,3103,646],{"stretchy":640},[635,3105,1113],{"mathvariant":1111,"lspace":1112,"rspace":1112},[635,3107,977],{},[587,3109,1104],{},[635,3111,1482],{},[1098,3113,3114,3116],{},[701,3115,1835],{},[584,3117,3118,3120,3122],{},[587,3119,1104],{},[635,3121,2313],{},[701,3123,703],{},[591,3125,3126],{"encoding":593},"(2^x)' = x \\cdot 2^{x-1}",[568,3128,3130,3209,3228],{"className":3129,"ariaHidden":598},[597],[568,3131,3133,3136,3139,3168,3200,3203,3206],{"className":3132},[602],[568,3134],{"className":3135,"style":1134},[606],[568,3137,641],{"className":3138},[667],[568,3140,3142,3145],{"className":3141},[611],[568,3143,1835],{"className":3144},[611],[568,3146,3148],{"className":3147},[1147],[568,3149,3151],{"className":3150},[1151],[568,3152,3154],{"className":3153},[1155],[568,3155,3157],{"className":3156,"style":1160},[1159],[568,3158,3159,3162],{"style":1163},[568,3160],{"className":3161,"style":1168},[1167],[568,3163,3165],{"className":3164},[1172,1173,1174,1175],[568,3166,1104],{"className":3167},[611,612,1175],[568,3169,3171,3174],{"className":3170},[674],[568,3172,646],{"className":3173},[674],[568,3175,3177],{"className":3176},[1147],[568,3178,3180],{"className":3179},[1151],[568,3181,3183],{"className":3182},[1155],[568,3184,3186],{"className":3185,"style":1197},[1159],[568,3187,3188,3191],{"style":1163},[568,3189],{"className":3190,"style":1168},[1167],[568,3192,3194],{"className":3193},[1172,1173,1174,1175],[568,3195,3197],{"className":3196},[611,1175],[568,3198,1113],{"className":3199},[611,1175],[568,3201],{"className":3202,"style":724},[723],[568,3204,977],{"className":3205},[728],[568,3207],{"className":3208,"style":724},[723],[568,3210,3212,3216,3219,3222,3225],{"className":3211},[602],[568,3213],{"className":3214,"style":3215},[606],"height:0.4445em;",[568,3217,1104],{"className":3218},[611,612],[568,3220],{"className":3221,"style":1703},[723],[568,3223,1482],{"className":3224},[1707],[568,3226],{"className":3227,"style":1703},[723],[568,3229,3231,3235],{"className":3230},[602],[568,3232],{"className":3233,"style":3234},[606],"height:0.8141em;",[568,3236,3238,3241],{"className":3237},[611],[568,3239,1835],{"className":3240},[611],[568,3242,3244],{"className":3243},[1147],[568,3245,3247],{"className":3246},[1151],[568,3248,3250],{"className":3249},[1155],[568,3251,3253],{"className":3252,"style":3234},[1159],[568,3254,3255,3258],{"style":1163},[568,3256],{"className":3257,"style":1168},[1167],[568,3259,3261],{"className":3260},[1172,1173,1174,1175],[568,3262,3264,3267,3270],{"className":3263},[611,1175],[568,3265,1104],{"className":3266},[611,612,1175],[568,3268,2313],{"className":3269},[1707,1175],[568,3271,703],{"className":3272},[611,1175]," ist falsch.",[680,3275,3276,3277,3322,3323,3477,3478,675],{},"Den Faktor ",[568,3278,3280,3301],{"className":3279},[571],[568,3281,3283],{"className":3282},[575],[577,3284,3285],{"xmlns":579},[581,3286,3287,3299],{},[584,3288,3289,3291,3293,3295,3297],{},[587,3290,633],{},[635,3292,637],{},[635,3294,641],{"stretchy":640},[587,3296,589],{},[635,3298,646],{"stretchy":640},[591,3300,649],{"encoding":593},[568,3302,3304],{"className":3303,"ariaHidden":598},[597],[568,3305,3307,3310,3313,3316,3319],{"className":3306},[602],[568,3308],{"className":3309,"style":659},[606],[568,3311,633],{"className":3312},[663],[568,3314,641],{"className":3315},[667],[568,3317,589],{"className":3318},[611,612],[568,3320,646],{"className":3321},[674]," vergessen und ",[568,3324,3326,3360],{"className":3325},[571],[568,3327,3329],{"className":3328},[575],[577,3330,3331],{"xmlns":579},[581,3332,3333,3357],{},[584,3334,3335,3337,3343,3349,3351],{},[635,3336,641],{"stretchy":640},[1098,3338,3339,3341],{},[701,3340,1835],{},[587,3342,1104],{},[1098,3344,3345,3347],{},[635,3346,646],{"stretchy":640},[635,3348,1113],{"mathvariant":1111,"lspace":1112,"rspace":1112},[635,3350,977],{},[1098,3352,3353,3355],{},[701,3354,1835],{},[587,3356,1104],{},[591,3358,3359],{"encoding":593},"(2^x)' = 2^x",[568,3361,3363,3442],{"className":3362,"ariaHidden":598},[597],[568,3364,3366,3369,3372,3401,3433,3436,3439],{"className":3365},[602],[568,3367],{"className":3368,"style":1134},[606],[568,3370,641],{"className":3371},[667],[568,3373,3375,3378],{"className":3374},[611],[568,3376,1835],{"className":3377},[611],[568,3379,3381],{"className":3380},[1147],[568,3382,3384],{"className":3383},[1151],[568,3385,3387],{"className":3386},[1155],[568,3388,3390],{"className":3389,"style":1160},[1159],[568,3391,3392,3395],{"style":1163},[568,3393],{"className":3394,"style":1168},[1167],[568,3396,3398],{"className":3397},[1172,1173,1174,1175],[568,3399,1104],{"className":3400},[611,612,1175],[568,3402,3404,3407],{"className":3403},[674],[568,3405,646],{"className":3406},[674],[568,3408,3410],{"className":3409},[1147],[568,3411,3413],{"className":3412},[1151],[568,3414,3416],{"className":3415},[1155],[568,3417,3419],{"className":3418,"style":1197},[1159],[568,3420,3421,3424],{"style":1163},[568,3422],{"className":3423,"style":1168},[1167],[568,3425,3427],{"className":3426},[1172,1173,1174,1175],[568,3428,3430],{"className":3429},[611,1175],[568,3431,1113],{"className":3432},[611,1175],[568,3434],{"className":3435,"style":724},[723],[568,3437,977],{"className":3438},[728],[568,3440],{"className":3441,"style":724},[723],[568,3443,3445,3448],{"className":3444},[602],[568,3446],{"className":3447,"style":1160},[606],[568,3449,3451,3454],{"className":3450},[611],[568,3452,1835],{"className":3453},[611],[568,3455,3457],{"className":3456},[1147],[568,3458,3460],{"className":3459},[1151],[568,3461,3463],{"className":3462},[1155],[568,3464,3466],{"className":3465,"style":1160},[1159],[568,3467,3468,3471],{"style":1163},[568,3469],{"className":3470,"style":1168},[1167],[568,3472,3474],{"className":3473},[1172,1173,1174,1175],[568,3475,1104],{"className":3476},[611,612,1175]," schreiben. Das gilt nur für die Basis ",[568,3479,3481,3494],{"className":3480},[571],[568,3482,3484],{"className":3483},[575],[577,3485,3486],{"xmlns":579},[581,3487,3488,3492],{},[584,3489,3490],{},[587,3491,980],{},[591,3493,980],{"encoding":593},[568,3495,3497],{"className":3496,"ariaHidden":598},[597],[568,3498,3500,3503],{"className":3499},[602],[568,3501],{"className":3502,"style":607},[606],[568,3504,980],{"className":3505},[611,612],[680,3507,3508,3509,3554,3555,675],{},"Den Zehnerlogarithmus statt des natürlichen Logarithmus verwenden. Der Faktor ist ",[568,3510,3512,3533],{"className":3511},[571],[568,3513,3515],{"className":3514},[575],[577,3516,3517],{"xmlns":579},[581,3518,3519,3531],{},[584,3520,3521,3523,3525,3527,3529],{},[587,3522,633],{},[635,3524,637],{},[635,3526,641],{"stretchy":640},[587,3528,589],{},[635,3530,646],{"stretchy":640},[591,3532,649],{"encoding":593},[568,3534,3536],{"className":3535,"ariaHidden":598},[597],[568,3537,3539,3542,3545,3548,3551],{"className":3538},[602],[568,3540],{"className":3541,"style":659},[606],[568,3543,633],{"className":3544},[663],[568,3546,641],{"className":3547},[667],[568,3549,589],{"className":3550},[611,612],[568,3552,646],{"className":3553},[674],", nicht ",[568,3556,3558,3581],{"className":3557},[571],[568,3559,3561],{"className":3560},[575],[577,3562,3563],{"xmlns":579},[581,3564,3565,3578],{},[584,3566,3567,3570,3572,3574,3576],{},[587,3568,3569],{},"lg",[635,3571,637],{},[635,3573,641],{"stretchy":640},[587,3575,589],{},[635,3577,646],{"stretchy":640},[591,3579,3580],{"encoding":593},"\\lg(a)",[568,3582,3584],{"className":3583,"ariaHidden":598},[597],[568,3585,3587,3590,3597,3600,3603],{"className":3586},[602],[568,3588],{"className":3589,"style":659},[606],[568,3591,1400,3593],{"className":3592},[663],[568,3594,3596],{"style":3595},"margin-right:0.0139em;","g",[568,3598,641],{"className":3599},[667],[568,3601,589],{"className":3602},[611,612],[568,3604,646],{"className":3605},[674],{"title":3607,"searchDepth":3608,"depth":3608,"links":3609},"",2,[3610,3611,3612,3613],{"id":561,"depth":3608,"text":562},{"id":1258,"depth":3608,"text":1259},{"id":1803,"depth":3608,"text":1804},{"id":3073,"depth":3608,"text":3074},[3615,3618,3620,3623,3626,3629,3632],{"lhs":3616,"rhs":3617},"a^x","exp(x*log(a))",{"lhs":3619,"rhs":769},"round((a^(x+1e-5) - a^(x-1e-5))\u002F(2e-5) - log(a)*a^x, 6)",{"lhs":3621,"rhs":3622},"log(2)*2^3","8*log(2)",{"lhs":3624,"rhs":3625},"round(8*log(2), 3)","5.545",{"lhs":3627,"rhs":3628},"round(log(0.5), 4)","-0.6931",{"lhs":3630,"rhs":3631},"100*log(1.05)*1.05^0","100*log(1.05)",{"lhs":3633,"rhs":3634},"round(100*log(1.05), 2)","4.88","a > 0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a > 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\">a\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-exp-base","f(x) = a^x \\;\\Rightarrow\\; f'(x) = \\ln(a) \\cdot a^x","\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>a\u003C\u002Fmi>\u003Cmi>x\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 stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>ln\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmsup>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f(x) = a^x \\;\\Rightarrow\\; f'(x) = \\ln(a) \\cdot a^x\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" 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