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",[580,671,673,686],{"className":672},[583],[580,674,676],{"className":675},[587],[589,677,678],{"xmlns":591},[593,679,680,684],{},[596,681,682],{},[599,683,601],{},[611,685,601],{"encoding":613},[580,687,689],{"className":688,"ariaHidden":619},[618],[580,690,692,696],{"className":691},[623],[580,693],{"className":694,"style":695},[627],"height:0.4306em;",[580,697,601],{"className":698},[632,633]," ist eine feste irrationale Zahl wie ",[580,701,703,718],{"className":702},[583],[580,704,706],{"className":705},[587],[589,707,708],{"xmlns":591},[593,709,710,715],{},[596,711,712],{},[599,713,714],{},"π",[611,716,717],{"encoding":613},"\\pi",[580,719,721],{"className":720,"ariaHidden":619},[618],[580,722,724,727],{"className":723},[623],[580,725],{"className":726,"style":695},[627],[580,728,714],{"className":729,"style":730},[632,633],"margin-right:0.0359em;",", keine Variable.",[564,733,734,735,763,764,767,768,924,925,953],{},"Die Basis ",[580,736,738,751],{"className":737},[583],[580,739,741],{"className":740},[587],[589,742,743],{"xmlns":591},[593,744,745,749],{},[596,746,747],{},[599,748,601],{},[611,750,601],{"encoding":613},[580,752,754],{"className":753,"ariaHidden":619},[618],[580,755,757,760],{"className":756},[623],[580,758],{"className":759,"style":695},[627],[580,761,601],{"className":762},[632,633]," ist deshalb besonders, weil die e-Funktion ",[568,765,766],{},"ihre eigene Ableitung"," ist: ",[580,769,771,813],{"className":770},[583],[580,772,774],{"className":773},[587],[589,775,776],{"xmlns":591},[593,777,778,810],{},[596,779,780,791,795,798,801,804],{},[781,782,783,786],"msup",{},[599,784,785],{},"f",[603,787,790],{"mathvariant":788,"lspace":789,"rspace":789},"normal","0em","′",[603,792,794],{"stretchy":793},"false","(",[599,796,797],{},"x",[603,799,800],{"stretchy":793},")",[603,802,803],{},"=",[781,805,806,808],{},[599,807,601],{},[599,809,797],{},[611,811,812],{"encoding":613},"f'(x) = e^x",[580,814,816,888],{"className":815,"ariaHidden":619},[618],[580,817,819,823,868,872,875,879,882,885],{"className":818},[623],[580,820],{"className":821,"style":822},[627],"height:1.0019em;vertical-align:-0.25em;",[580,824,826,830],{"className":825},[632],[580,827,785],{"className":828,"style":829},[632,633],"margin-right:0.1076em;",[580,831,834],{"className":832},[833],"msupsub",[580,835,838],{"className":836},[837],"vlist-t",[580,839,842],{"className":840},[841],"vlist-r",[580,843,847],{"className":844,"style":846},[845],"vlist","height:0.7519em;",[580,848,850,855],{"style":849},"top:-3.063em;margin-right:0.05em;",[580,851],{"className":852,"style":854},[853],"pstrut","height:2.7em;",[580,856,862],{"className":857},[858,859,860,861],"sizing","reset-size6","size3","mtight",[580,863,865],{"className":864},[632,861],[580,866,790],{"className":867},[632,861],[580,869,794],{"className":870},[871],"mopen",[580,873,797],{"className":874},[632,633],[580,876,800],{"className":877},[878],"mclose",[580,880],{"className":881,"style":638},[637],[580,883,803],{"className":884},[642],[580,886],{"className":887,"style":638},[637],[580,889,891,895],{"className":890},[623],[580,892],{"className":893,"style":894},[627],"height:0.6644em;",[580,896,898,901],{"className":897},[632],[580,899,601],{"className":900},[632,633],[580,902,904],{"className":903},[833],[580,905,907],{"className":906},[837],[580,908,910],{"className":909},[841],[580,911,913],{"className":912,"style":894},[845],[580,914,915,918],{"style":849},[580,916],{"className":917,"style":854},[853],[580,919,921],{"className":920},[858,859,860,861],[580,922,797],{"className":923},[632,633,861],". An jeder Stelle ist die Steigung des Graphen also so groß wie der Funktionswert. Deshalb beschreibt man Wachstums- und Zerfallsvorgänge in der Oberstufe meist mit ",[580,926,928,941],{"className":927},[583],[580,929,931],{"className":930},[587],[589,932,933],{"xmlns":591},[593,934,935,939],{},[596,936,937],{},[599,938,601],{},[611,940,601],{"encoding":613},[580,942,944],{"className":943,"ariaHidden":619},[618],[580,945,947,950],{"className":946},[623],[580,948],{"className":949,"style":695},[627],[580,951,601],{"className":952},[632,633],".",[564,955,956],{},"Eigenschaften:",[958,959,960,1096,1272,1275],"ul",{},[961,962,963,1033,1034,953],"li",{},[580,964,966,992],{"className":965},[583],[580,967,969],{"className":968},[587],[589,970,971],{"xmlns":591},[593,972,973,989],{},[596,974,975,977,979,982,984,986],{},[599,976,785],{},[603,978,794],{"stretchy":793},[607,980,981],{},"0",[603,983,800],{"stretchy":793},[603,985,803],{},[607,987,988],{},"1",[611,990,991],{"encoding":613},"f(0) = 1",[580,993,995,1023],{"className":994,"ariaHidden":619},[618],[580,996,998,1002,1005,1008,1011,1014,1017,1020],{"className":997},[623],[580,999],{"className":1000,"style":1001},[627],"height:1em;vertical-align:-0.25em;",[580,1003,785],{"className":1004,"style":829},[632,633],[580,1006,794],{"className":1007},[871],[580,1009,981],{"className":1010},[632],[580,1012,800],{"className":1013},[878],[580,1015],{"className":1016,"style":638},[637],[580,1018,803],{"className":1019},[642],[580,1021],{"className":1022,"style":638},[637],[580,1024,1026,1030],{"className":1025},[623],[580,1027],{"className":1028,"style":1029},[627],"height:0.6444em;",[580,1031,988],{"className":1032},[632],", der Graph schneidet die y-Achse in ",[580,1035,1037,1060],{"className":1036},[583],[580,1038,1040],{"className":1039},[587],[589,1041,1042],{"xmlns":591},[593,1043,1044,1057],{},[596,1045,1046,1048,1050,1053,1055],{},[603,1047,794],{"stretchy":793},[607,1049,981],{},[603,1051,1052],{},"∣",[607,1054,988],{},[603,1056,800],{"stretchy":793},[611,1058,1059],{"encoding":613},"(0 \\mid 1)",[580,1061,1063,1084],{"className":1062,"ariaHidden":619},[618],[580,1064,1066,1069,1072,1075,1078,1081],{"className":1065},[623],[580,1067],{"className":1068,"style":1001},[627],[580,1070,794],{"className":1071},[871],[580,1073,981],{"className":1074},[632],[580,1076],{"className":1077,"style":638},[637],[580,1079,1052],{"className":1080},[642],[580,1082],{"className":1083,"style":638},[637],[580,1085,1087,1090,1093],{"className":1086},[623],[580,1088],{"className":1089,"style":1001},[627],[580,1091,988],{"className":1092},[632],[580,1094,800],{"className":1095},[878],[961,1097,1098,1181,1182,1210,1211,1271],{},[580,1099,1101,1124],{"className":1100},[583],[580,1102,1104],{"className":1103},[587],[589,1105,1106],{"xmlns":591},[593,1107,1108,1121],{},[596,1109,1110,1116,1119],{},[781,1111,1112,1114],{},[599,1113,601],{},[599,1115,797],{},[603,1117,1118],{},">",[607,1120,981],{},[611,1122,1123],{"encoding":613},"e^x > 0",[580,1125,1127,1172],{"className":1126,"ariaHidden":619},[618],[580,1128,1130,1134,1163,1166,1169],{"className":1129},[623],[580,1131],{"className":1132,"style":1133},[627],"height:0.7035em;vertical-align:-0.0391em;",[580,1135,1137,1140],{"className":1136},[632],[580,1138,601],{"className":1139},[632,633],[580,1141,1143],{"className":1142},[833],[580,1144,1146],{"className":1145},[837],[580,1147,1149],{"className":1148},[841],[580,1150,1152],{"className":1151,"style":894},[845],[580,1153,1154,1157],{"style":849},[580,1155],{"className":1156,"style":854},[853],[580,1158,1160],{"className":1159},[858,859,860,861],[580,1161,797],{"className":1162},[632,633,861],[580,1164],{"className":1165,"style":638},[637],[580,1167,1118],{"className":1168},[642],[580,1170],{"className":1171,"style":638},[637],[580,1173,1175,1178],{"className":1174},[623],[580,1176],{"className":1177,"style":1029},[627],[580,1179,981],{"className":1180},[632]," für alle ",[580,1183,1185,1198],{"className":1184},[583],[580,1186,1188],{"className":1187},[587],[589,1189,1190],{"xmlns":591},[593,1191,1192,1196],{},[596,1193,1194],{},[599,1195,797],{},[611,1197,797],{"encoding":613},[580,1199,1201],{"className":1200,"ariaHidden":619},[618],[580,1202,1204,1207],{"className":1203},[623],[580,1205],{"className":1206,"style":695},[627],[580,1208,797],{"className":1209},[632,633],"; es gibt keine Nullstelle. Für ",[580,1212,1214,1237],{"className":1213},[583],[580,1215,1217],{"className":1216},[587],[589,1218,1219],{"xmlns":591},[593,1220,1221,1234],{},[596,1222,1223,1225,1228,1231],{},[599,1224,797],{},[603,1226,1227],{},"→",[603,1229,1230],{},"−",[599,1232,1233],{"mathvariant":788},"∞",[611,1235,1236],{"encoding":613},"x \\to -\\infty",[580,1238,1240,1258],{"className":1239,"ariaHidden":619},[618],[580,1241,1243,1246,1249,1252,1255],{"className":1242},[623],[580,1244],{"className":1245,"style":695},[627],[580,1247,797],{"className":1248},[632,633],[580,1250],{"className":1251,"style":638},[637],[580,1253,1227],{"className":1254},[642],[580,1256],{"className":1257,"style":638},[637],[580,1259,1261,1265,1268],{"className":1260},[623],[580,1262],{"className":1263,"style":1264},[627],"height:0.6667em;vertical-align:-0.0833em;",[580,1266,1230],{"className":1267},[632],[580,1269,1233],{"className":1270},[632]," nähert sich der Graph der x-Achse.",[961,1273,1274],{},"Der Graph steigt überall.",[961,1276,1277,1278,953],{},"Die Umkehrfunktion ist der natürliche Logarithmus: ",[580,1279,1281,1313],{"className":1280},[583],[580,1282,1284],{"className":1283},[587],[589,1285,1286],{"xmlns":591},[593,1287,1288,1310],{},[596,1289,1290,1293,1296,1298,1304,1306,1308],{},[599,1291,1292],{},"ln",[603,1294,1295],{},"⁡",[603,1297,794],{"stretchy":793},[781,1299,1300,1302],{},[599,1301,601],{},[599,1303,797],{},[603,1305,800],{"stretchy":793},[603,1307,803],{},[599,1309,797],{},[611,1311,1312],{"encoding":613},"\\ln(e^x) = x",[580,1314,1316,1370],{"className":1315,"ariaHidden":619},[618],[580,1317,1319,1322,1326,1329,1358,1361,1364,1367],{"className":1318},[623],[580,1320],{"className":1321,"style":1001},[627],[580,1323,1292],{"className":1324},[1325],"mop",[580,1327,794],{"className":1328},[871],[580,1330,1332,1335],{"className":1331},[632],[580,1333,601],{"className":1334},[632,633],[580,1336,1338],{"className":1337},[833],[580,1339,1341],{"className":1340},[837],[580,1342,1344],{"className":1343},[841],[580,1345,1347],{"className":1346,"style":894},[845],[580,1348,1349,1352],{"style":849},[580,1350],{"className":1351,"style":854},[853],[580,1353,1355],{"className":1354},[858,859,860,861],[580,1356,797],{"className":1357},[632,633,861],[580,1359,800],{"className":1360},[878],[580,1362],{"className":1363,"style":638},[637],[580,1365,803],{"className":1366},[642],[580,1368],{"className":1369,"style":638},[637],[580,1371,1373,1376],{"className":1372},[623],[580,1374],{"className":1375,"style":695},[627],[580,1377,797],{"className":1378},[632,633],[564,1380,1381,1382,1410,1411,1518],{},"Jede Exponentialfunktion mit positiver Basis lässt sich mit ",[580,1383,1385,1398],{"className":1384},[583],[580,1386,1388],{"className":1387},[587],[589,1389,1390],{"xmlns":591},[593,1391,1392,1396],{},[596,1393,1394],{},[599,1395,601],{},[611,1397,601],{"encoding":613},[580,1399,1401],{"className":1400,"ariaHidden":619},[618],[580,1402,1404,1407],{"className":1403},[623],[580,1405],{"className":1406,"style":695},[627],[580,1408,601],{"className":1409},[632,633]," schreiben, weil ",[580,1412,1414,1443],{"className":1413},[583],[580,1415,1417],{"className":1416},[587],[589,1418,1419],{"xmlns":591},[593,1420,1421,1440],{},[596,1422,1423,1426,1428],{},[599,1424,1425],{},"a",[603,1427,803],{},[781,1429,1430,1432],{},[599,1431,601],{},[596,1433,1434,1436,1438],{},[599,1435,1292],{},[603,1437,1295],{},[599,1439,1425],{},[611,1441,1442],{"encoding":613},"a = e^{\\ln a}",[580,1444,1446,1464],{"className":1445,"ariaHidden":619},[618],[580,1447,1449,1452,1455,1458,1461],{"className":1448},[623],[580,1450],{"className":1451,"style":695},[627],[580,1453,1425],{"className":1454},[632,633],[580,1456],{"className":1457,"style":638},[637],[580,1459,803],{"className":1460},[642],[580,1462],{"className":1463,"style":638},[637],[580,1465,1467,1471],{"className":1466},[623],[580,1468],{"className":1469,"style":1470},[627],"height:0.8491em;",[580,1472,1474,1477],{"className":1473},[632],[580,1475,601],{"className":1476},[632,633],[580,1478,1480],{"className":1479},[833],[580,1481,1483],{"className":1482},[837],[580,1484,1486],{"className":1485},[841],[580,1487,1489],{"className":1488,"style":1470},[845],[580,1490,1491,1494],{"style":849},[580,1492],{"className":1493,"style":854},[853],[580,1495,1497],{"className":1496},[858,859,860,861],[580,1498,1500,1511,1515],{"className":1499},[632,861],[580,1501,1503,1507],{"className":1502},[1325,861],[580,1504,1506],{"className":1505},[861],"l",[580,1508,1510],{"className":1509},[861],"n",[580,1512],{"className":1513,"style":1514},[637,861],"margin-right:0.1952em;",[580,1516,1425],{"className":1517},[632,633,861]," gilt:",[580,1520,1523],{"className":1521},[1522],"katex-display",[580,1524,1526,1577],{"className":1525},[583],[580,1527,1529],{"className":1528},[587],[589,1530,1532],{"xmlns":591,"display":1531},"block",[593,1533,1534,1574],{},[596,1535,1536,1542,1544,1561,1564,1566,1568,1570,1572],{},[781,1537,1538,1540],{},[599,1539,1425],{},[599,1541,797],{},[603,1543,803],{},[781,1545,1546,1548],{},[599,1547,601],{},[596,1549,1550,1552,1555,1557,1559],{},[599,1551,797],{},[603,1553,1554],{},"⋅",[599,1556,1292],{},[603,1558,1295],{},[599,1560,1425],{},[637,1562],{"width":1563},"1em",[603,1565,794],{"stretchy":793},[599,1567,1425],{},[603,1569,1118],{},[607,1571,981],{},[603,1573,800],{"stretchy":793},[611,1575,1576],{"encoding":613},"a^x = e^{x \\cdot \\ln a} \\quad (a > 0)",[580,1578,1580,1626,1704],{"className":1579,"ariaHidden":619},[618],[580,1581,1583,1587,1617,1620,1623],{"className":1582},[623],[580,1584],{"className":1585,"style":1586},[627],"height:0.7144em;",[580,1588,1590,1593],{"className":1589},[632],[580,1591,1425],{"className":1592},[632,633],[580,1594,1596],{"className":1595},[833],[580,1597,1599],{"className":1598},[837],[580,1600,1602],{"className":1601},[841],[580,1603,1605],{"className":1604,"style":1586},[845],[580,1606,1608,1611],{"style":1607},"top:-3.113em;margin-right:0.05em;",[580,1609],{"className":1610,"style":854},[853],[580,1612,1614],{"className":1613},[858,859,860,861],[580,1615,797],{"className":1616},[632,633,861],[580,1618],{"className":1619,"style":638},[637],[580,1621,803],{"className":1622},[642],[580,1624],{"className":1625,"style":638},[637],[580,1627,1629,1633,1685,1689,1692,1695,1698,1701],{"className":1628},[623],[580,1630],{"className":1631,"style":1632},[627],"height:1.1491em;vertical-align:-0.25em;",[580,1634,1636,1639],{"className":1635},[632],[580,1637,601],{"className":1638},[632,633],[580,1640,1642],{"className":1641},[833],[580,1643,1645],{"className":1644},[837],[580,1646,1648],{"className":1647},[841],[580,1649,1652],{"className":1650,"style":1651},[845],"height:0.8991em;",[580,1653,1654,1657],{"style":1607},[580,1655],{"className":1656,"style":854},[853],[580,1658,1660],{"className":1659},[858,859,860,861],[580,1661,1663,1666,1670,1679,1682],{"className":1662},[632,861],[580,1664,797],{"className":1665},[632,633,861],[580,1667,1554],{"className":1668},[1669,861],"mbin",[580,1671,1673,1676],{"className":1672},[1325,861],[580,1674,1506],{"className":1675},[861],[580,1677,1510],{"className":1678},[861],[580,1680],{"className":1681,"style":1514},[637,861],[580,1683,1425],{"className":1684},[632,633,861],[580,1686],{"className":1687,"style":1688},[637],"margin-right:1em;",[580,1690,794],{"className":1691},[871],[580,1693,1425],{"className":1694},[632,633],[580,1696],{"className":1697,"style":638},[637],[580,1699,1118],{"className":1700},[642],[580,1702],{"className":1703,"style":638},[637],[580,1705,1707,1710,1713],{"className":1706},[623],[580,1708],{"className":1709,"style":1001},[627],[580,1711,981],{"className":1712},[632],[580,1714,800],{"className":1715},[878],[559,1717,1719],{"id":1718},"beispiele","Beispiele",[564,1721,1722],{},"Werte der e-Funktion mit dem Taschenrechner:",[580,1724,1726],{"className":1725},[1522],[580,1727,1729,1781],{"className":1728},[583],[580,1730,1732],{"className":1731},[587],[589,1733,1734],{"xmlns":591,"display":1531},[593,1735,1736,1778],{},[596,1737,1738,1744,1746,1749,1751,1754,1764,1766,1773,1775],{},[781,1739,1740,1742],{},[599,1741,601],{},[607,1743,656],{},[603,1745,605],{},[607,1747,1748],{},"7,39",[603,1750,664],{"separator":619},[637,1752],{"width":1753},"2em",[781,1755,1756,1758],{},[599,1757,601],{},[596,1759,1760,1762],{},[603,1761,1230],{},[607,1763,988],{},[603,1765,803],{},[1767,1768,1769,1771],"mfrac",{},[607,1770,988],{},[599,1772,601],{},[603,1774,605],{},[607,1776,1777],{},"0,3679",[611,1779,1780],{"encoding":613},"e^2 \\approx 7{,}39, \\qquad e^{-1} = \\frac{1}{e} \\approx 0{,}3679",[580,1782,1784,1829,1905,1995],{"className":1783,"ariaHidden":619},[618],[580,1785,1787,1791,1820,1823,1826],{"className":1786},[623],[580,1788],{"className":1789,"style":1790},[627],"height:0.8641em;",[580,1792,1794,1797],{"className":1793},[632],[580,1795,601],{"className":1796},[632,633],[580,1798,1800],{"className":1799},[833],[580,1801,1803],{"className":1802},[837],[580,1804,1806],{"className":1805},[841],[580,1807,1809],{"className":1808,"style":1790},[845],[580,1810,1811,1814],{"style":1607},[580,1812],{"className":1813,"style":854},[853],[580,1815,1817],{"className":1816},[858,859,860,861],[580,1818,656],{"className":1819},[632,861],[580,1821],{"className":1822,"style":638},[637],[580,1824,605],{"className":1825},[642],[580,1827],{"className":1828,"style":638},[637],[580,1830,1832,1836,1840,1846,1850,1853,1857,1861,1896,1899,1902],{"className":1831},[623],[580,1833],{"className":1834,"style":1835},[627],"height:1.0585em;vertical-align:-0.1944em;",[580,1837,1839],{"className":1838},[632],"7",[580,1841,1843],{"className":1842},[632],[580,1844,664],{"className":1845},[663],[580,1847,1849],{"className":1848},[632],"39",[580,1851,664],{"className":1852},[663],[580,1854],{"className":1855,"style":1856},[637],"margin-right:2em;",[580,1858],{"className":1859,"style":1860},[637],"margin-right:0.1667em;",[580,1862,1864,1867],{"className":1863},[632],[580,1865,601],{"className":1866},[632,633],[580,1868,1870],{"className":1869},[833],[580,1871,1873],{"className":1872},[837],[580,1874,1876],{"className":1875},[841],[580,1877,1879],{"className":1878,"style":1790},[845],[580,1880,1881,1884],{"style":1607},[580,1882],{"className":1883,"style":854},[853],[580,1885,1887],{"className":1886},[858,859,860,861],[580,1888,1890,1893],{"className":1889},[632,861],[580,1891,1230],{"className":1892},[632,861],[580,1894,988],{"className":1895},[632,861],[580,1897],{"className":1898,"style":638},[637],[580,1900,803],{"className":1901},[642],[580,1903],{"className":1904,"style":638},[637],[580,1906,1908,1912,1986,1989,1992],{"className":1907},[623],[580,1909],{"className":1910,"style":1911},[627],"height:2.0074em;vertical-align:-0.686em;",[580,1913,1915,1919,1983],{"className":1914},[632],[580,1916],{"className":1917},[871,1918],"nulldelimiter",[580,1920,1922],{"className":1921},[1767],[580,1923,1926,1974],{"className":1924},[837,1925],"vlist-t2",[580,1927,1929,1969],{"className":1928},[841],[580,1930,1933,1946,1957],{"className":1931,"style":1932},[845],"height:1.3214em;",[580,1934,1936,1940],{"style":1935},"top:-2.314em;",[580,1937],{"className":1938,"style":1939},[853],"height:3em;",[580,1941,1943],{"className":1942},[632],[580,1944,601],{"className":1945},[632,633],[580,1947,1949,1952],{"style":1948},"top:-3.23em;",[580,1950],{"className":1951,"style":1939},[853],[580,1953],{"className":1954,"style":1956},[1955],"frac-line","border-bottom-width:0.04em;",[580,1958,1960,1963],{"style":1959},"top:-3.677em;",[580,1961],{"className":1962,"style":1939},[853],[580,1964,1966],{"className":1965},[632],[580,1967,988],{"className":1968},[632],[580,1970,1973],{"className":1971},[1972],"vlist-s","​",[580,1975,1977],{"className":1976},[841],[580,1978,1981],{"className":1979,"style":1980},[845],"height:0.686em;",[580,1982],{},[580,1984],{"className":1985},[878,1918],[580,1987],{"className":1988,"style":638},[637],[580,1990,605],{"className":1991},[642],[580,1993],{"className":1994,"style":638},[637],[580,1996,1998,2001,2004,2010],{"className":1997},[623],[580,1999],{"className":2000,"style":652},[627],[580,2002,981],{"className":2003},[632],[580,2005,2007],{"className":2006},[632],[580,2008,664],{"className":2009},[663],[580,2011,2013],{"className":2012},[632],"3679",[564,2015,2016,2017,2045,2046,2119],{},"Umschreiben auf die Basis ",[580,2018,2020,2033],{"className":2019},[583],[580,2021,2023],{"className":2022},[587],[589,2024,2025],{"xmlns":591},[593,2026,2027,2031],{},[596,2028,2029],{},[599,2030,601],{},[611,2032,601],{"encoding":613},[580,2034,2036],{"className":2035,"ariaHidden":619},[618],[580,2037,2039,2042],{"className":2038},[623],[580,2040],{"className":2041,"style":695},[627],[580,2043,601],{"className":2044},[632,633],": Mit ",[580,2047,2049,2072],{"className":2048},[583],[580,2050,2052],{"className":2051},[587],[589,2053,2054],{"xmlns":591},[593,2055,2056,2069],{},[596,2057,2058,2060,2062,2064,2066],{},[599,2059,1292],{},[603,2061,1295],{},[607,2063,656],{},[603,2065,605],{},[607,2067,2068],{},"0,6931",[611,2070,2071],{"encoding":613},"\\ln 2 \\approx 0{,}6931",[580,2073,2075,2100],{"className":2074,"ariaHidden":619},[618],[580,2076,2078,2082,2085,2088,2091,2094,2097],{"className":2077},[623],[580,2079],{"className":2080,"style":2081},[627],"height:0.6944em;",[580,2083,1292],{"className":2084},[1325],[580,2086],{"className":2087,"style":1860},[637],[580,2089,656],{"className":2090},[632],[580,2092],{"className":2093,"style":638},[637],[580,2095,605],{"className":2096},[642],[580,2098],{"className":2099,"style":638},[637],[580,2101,2103,2106,2109,2115],{"className":2102},[623],[580,2104],{"className":2105,"style":652},[627],[580,2107,981],{"className":2108},[632],[580,2110,2112],{"className":2111},[632],[580,2113,664],{"className":2114},[663],[580,2116,2118],{"className":2117},[632],"6931"," wird",[580,2121,2123],{"className":2122},[1522],[580,2124,2126,2187],{"className":2125},[583],[580,2127,2129],{"className":2128},[587],[589,2130,2131],{"xmlns":591,"display":1531},[593,2132,2133,2184],{},[596,2134,2135,2138,2140,2146,2148,2150,2152,2168,2170,2172,2174],{},[607,2136,2137],{},"3",[603,2139,1554],{},[781,2141,2142,2144],{},[607,2143,656],{},[599,2145,797],{},[603,2147,803],{},[607,2149,2137],{},[603,2151,1554],{},[781,2153,2154,2156],{},[599,2155,601],{},[596,2157,2158,2160,2162,2164,2166],{},[599,2159,1292],{},[603,2161,1295],{},[607,2163,656],{},[603,2165,1554],{},[599,2167,797],{},[603,2169,605],{},[607,2171,2137],{},[603,2173,1554],{},[781,2175,2176,2178],{},[599,2177,601],{},[596,2179,2180,2182],{},[607,2181,2068],{},[599,2183,797],{},[611,2185,2186],{"encoding":613},"3 \\cdot 2^x = 3 \\cdot e^{\\ln 2 \\cdot x} \\approx 3 \\cdot e^{0{,}6931 x}",[580,2188,2190,2209,2253,2271,2336,2354],{"className":2189,"ariaHidden":619},[618],[580,2191,2193,2196,2199,2203,2206],{"className":2192},[623],[580,2194],{"className":2195,"style":1029},[627],[580,2197,2137],{"className":2198},[632],[580,2200],{"className":2201,"style":2202},[637],"margin-right:0.2222em;",[580,2204,1554],{"className":2205},[1669],[580,2207],{"className":2208,"style":2202},[637],[580,2210,2212,2215,2244,2247,2250],{"className":2211},[623],[580,2213],{"className":2214,"style":1586},[627],[580,2216,2218,2221],{"className":2217},[632],[580,2219,656],{"className":2220},[632],[580,2222,2224],{"className":2223},[833],[580,2225,2227],{"className":2226},[837],[580,2228,2230],{"className":2229},[841],[580,2231,2233],{"className":2232,"style":1586},[845],[580,2234,2235,2238],{"style":1607},[580,2236],{"className":2237,"style":854},[853],[580,2239,2241],{"className":2240},[858,859,860,861],[580,2242,797],{"className":2243},[632,633,861],[580,2245],{"className":2246,"style":638},[637],[580,2248,803],{"className":2249},[642],[580,2251],{"className":2252,"style":638},[637],[580,2254,2256,2259,2262,2265,2268],{"className":2255},[623],[580,2257],{"className":2258,"style":1029},[627],[580,2260,2137],{"className":2261},[632],[580,2263],{"className":2264,"style":2202},[637],[580,2266,1554],{"className":2267},[1669],[580,2269],{"className":2270,"style":2202},[637],[580,2272,2274,2277,2327,2330,2333],{"className":2273},[623],[580,2275],{"className":2276,"style":1651},[627],[580,2278,2280,2283],{"className":2279},[632],[580,2281,601],{"className":2282},[632,633],[580,2284,2286],{"className":2285},[833],[580,2287,2289],{"className":2288},[837],[580,2290,2292],{"className":2291},[841],[580,2293,2295],{"className":2294,"style":1651},[845],[580,2296,2297,2300],{"style":1607},[580,2298],{"className":2299,"style":854},[853],[580,2301,2303],{"className":2302},[858,859,860,861],[580,2304,2306,2315,2318,2321,2324],{"className":2305},[632,861],[580,2307,2309,2312],{"className":2308},[1325,861],[580,2310,1506],{"className":2311},[861],[580,2313,1510],{"className":2314},[861],[580,2316],{"className":2317,"style":1514},[637,861],[580,2319,656],{"className":2320},[632,861],[580,2322,1554],{"className":2323},[1669,861],[580,2325,797],{"className":2326},[632,633,861],[580,2328],{"className":2329,"style":638},[637],[580,2331,605],{"className":2332},[642],[580,2334],{"className":2335,"style":638},[637],[580,2337,2339,2342,2345,2348,2351],{"className":2338},[623],[580,2340],{"className":2341,"style":1029},[627],[580,2343,2137],{"className":2344},[632],[580,2346],{"className":2347,"style":2202},[637],[580,2349,1554],{"className":2350},[1669],[580,2352],{"className":2353,"style":2202},[637],[580,2355,2357,2360],{"className":2356},[623],[580,2358],{"className":2359,"style":1790},[627],[580,2361,2363,2366],{"className":2362},[632],[580,2364,601],{"className":2365},[632,633],[580,2367,2369],{"className":2368},[833],[580,2370,2372],{"className":2371},[837],[580,2373,2375],{"className":2374},[841],[580,2376,2378],{"className":2377,"style":1790},[845],[580,2379,2380,2383],{"style":1607},[580,2381],{"className":2382,"style":854},[853],[580,2384,2386],{"className":2385},[858,859,860,861],[580,2387,2389,2392,2398,2401],{"className":2388},[632,861],[580,2390,981],{"className":2391},[632,861],[580,2393,2395],{"className":2394},[632,861],[580,2396,664],{"className":2397},[663,861],[580,2399,2118],{"className":2400},[632,861],[580,2402,797],{"className":2403},[632,633,861],[559,2405,2407],{"id":2406},"typische-fehler","Typische Fehler",[958,2409,2410,2667,2941],{},[961,2411,2412,2413,2567,2568,2666],{},"Beim Ableiten die Potenzregel anwenden: ",[580,2414,2416,2450],{"className":2415},[583],[580,2417,2419],{"className":2418},[587],[589,2420,2421],{"xmlns":591},[593,2422,2423,2447],{},[596,2424,2425,2427,2433,2439,2441],{},[603,2426,794],{"stretchy":793},[781,2428,2429,2431],{},[599,2430,601],{},[599,2432,797],{},[781,2434,2435,2437],{},[603,2436,800],{"stretchy":793},[603,2438,790],{"mathvariant":788,"lspace":789,"rspace":789},[603,2440,803],{},[781,2442,2443,2445],{},[599,2444,601],{},[599,2446,797],{},[611,2448,2449],{"encoding":613},"(e^x)' = e^x",[580,2451,2453,2532],{"className":2452,"ariaHidden":619},[618],[580,2454,2456,2459,2462,2491,2523,2526,2529],{"className":2455},[623],[580,2457],{"className":2458,"style":822},[627],[580,2460,794],{"className":2461},[871],[580,2463,2465,2468],{"className":2464},[632],[580,2466,601],{"className":2467},[632,633],[580,2469,2471],{"className":2470},[833],[580,2472,2474],{"className":2473},[837],[580,2475,2477],{"className":2476},[841],[580,2478,2480],{"className":2479,"style":894},[845],[580,2481,2482,2485],{"style":849},[580,2483],{"className":2484,"style":854},[853],[580,2486,2488],{"className":2487},[858,859,860,861],[580,2489,797],{"className":2490},[632,633,861],[580,2492,2494,2497],{"className":2493},[878],[580,2495,800],{"className":2496},[878],[580,2498,2500],{"className":2499},[833],[580,2501,2503],{"className":2502},[837],[580,2504,2506],{"className":2505},[841],[580,2507,2509],{"className":2508,"style":846},[845],[580,2510,2511,2514],{"style":849},[580,2512],{"className":2513,"style":854},[853],[580,2515,2517],{"className":2516},[858,859,860,861],[580,2518,2520],{"className":2519},[632,861],[580,2521,790],{"className":2522},[632,861],[580,2524],{"className":2525,"style":638},[637],[580,2527,803],{"className":2528},[642],[580,2530],{"className":2531,"style":638},[637],[580,2533,2535,2538],{"className":2534},[623],[580,2536],{"className":2537,"style":894},[627],[580,2539,2541,2544],{"className":2540},[632],[580,2542,601],{"className":2543},[632,633],[580,2545,2547],{"className":2546},[833],[580,2548,2550],{"className":2549},[837],[580,2551,2553],{"className":2552},[841],[580,2554,2556],{"className":2555,"style":894},[845],[580,2557,2558,2561],{"style":849},[580,2559],{"className":2560,"style":854},[853],[580,2562,2564],{"className":2563},[858,859,860,861],[580,2565,797],{"className":2566},[632,633,861],", nicht ",[580,2569,2571,2599],{"className":2570},[583],[580,2572,2574],{"className":2573},[587],[589,2575,2576],{"xmlns":591},[593,2577,2578,2596],{},[596,2579,2580,2582,2584],{},[599,2581,797],{},[603,2583,1554],{},[781,2585,2586,2588],{},[599,2587,601],{},[596,2589,2590,2592,2594],{},[599,2591,797],{},[603,2593,1230],{},[607,2595,988],{},[611,2597,2598],{"encoding":613},"x \\cdot e^{x-1}",[580,2600,2602,2621],{"className":2601,"ariaHidden":619},[618],[580,2603,2605,2609,2612,2615,2618],{"className":2604},[623],[580,2606],{"className":2607,"style":2608},[627],"height:0.4445em;",[580,2610,797],{"className":2611},[632,633],[580,2613],{"className":2614,"style":2202},[637],[580,2616,1554],{"className":2617},[1669],[580,2619],{"className":2620,"style":2202},[637],[580,2622,2624,2628],{"className":2623},[623],[580,2625],{"className":2626,"style":2627},[627],"height:0.8141em;",[580,2629,2631,2634],{"className":2630},[632],[580,2632,601],{"className":2633},[632,633],[580,2635,2637],{"className":2636},[833],[580,2638,2640],{"className":2639},[837],[580,2641,2643],{"className":2642},[841],[580,2644,2646],{"className":2645,"style":2627},[845],[580,2647,2648,2651],{"style":849},[580,2649],{"className":2650,"style":854},[853],[580,2652,2654],{"className":2653},[858,859,860,861],[580,2655,2657,2660,2663],{"className":2656},[632,861],[580,2658,797],{"className":2659},[632,633,861],[580,2661,1230],{"className":2662},[1669,861],[580,2664,988],{"className":2665},[632,861],". Die Variable steht im Exponenten, nicht in der Basis.",[961,2668,2669,2670,2567,2843,953],{},"Potenzgesetze falsch anwenden: ",[580,2671,2673,2711],{"className":2672},[583],[580,2674,2676],{"className":2675},[587],[589,2677,2678],{"xmlns":591},[593,2679,2680,2708],{},[596,2681,2682,2688,2690,2696,2698],{},[781,2683,2684,2686],{},[599,2685,601],{},[599,2687,797],{},[603,2689,1554],{},[781,2691,2692,2694],{},[599,2693,601],{},[599,2695,797],{},[603,2697,803],{},[781,2699,2700,2702],{},[599,2701,601],{},[596,2703,2704,2706],{},[607,2705,656],{},[599,2707,797],{},[611,2709,2710],{"encoding":613},"e^x \\cdot e^x = 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