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1",[580,1102,1104,1123],{"className":1103,"ariaHidden":610},[609],[580,1105,1107,1111,1114,1117,1120],{"className":1106},[614],[580,1108],{"className":1109,"style":1110},[618],"height:0.4306em;",[580,1112,660],{"className":1113},[623,719],[580,1115],{"className":1116,"style":736},[735],[580,1118,666],{"className":1119},[740],[580,1121],{"className":1122,"style":736},[735],[580,1124,1126,1129],{"className":1125},[614],[580,1127],{"className":1128,"style":619},[618],[580,1130,1097],{"className":1131},[623],":",[580,1134,1136],{"className":1135},[635],[580,1137,1139,1180],{"className":1138},[583],[580,1140,1142],{"className":1141},[587],[589,1143,1144],{"xmlns":591,"display":644},[593,1145,1146,1177],{},[596,1147,1148,1154,1156,1158,1160,1162,1164,1166,1168,1170,1172,1174],{},[671,1149,1150,1152],{},[650,1151,652],{},[654,1153,907],{"mathvariant":905,"lspace":906,"rspace":906},[654,1155,657],{"stretchy":656},[599,1157,1097],{},[654,1159,663],{"stretchy":656},[654,1161,666],{},[599,1163,918],{},[654,1165,680],{},[599,1167,677],{},[654,1169,692],{},[599,1171,695],{},[654,1173,666],{},[599,1175,1176],{},"15",[603,1178,1179],{"encoding":605},"f'(1) = 12 - 4 + 7 = 15",[580,1181,1183,1239,1257,1275,1293],{"className":1182,"ariaHidden":610},[609],[580,1184,1186,1189,1221,1224,1227,1230,1233,1236],{"className":1185},[614],[580,1187],{"className":1188,"style":947},[618],[580,1190,1192,1195],{"className":1191},[623],[580,1193,652],{"className":1194,"style":720},[623,719],[580,1196,1198],{"className":1197},[763],[580,1199,1201],{"className":1200},[767],[580,1202,1204],{"className":1203},[771],[580,1205,1207],{"className":1206,"style":966},[775],[580,1208,1209,1212],{"style":779},[580,1210],{"className":1211,"style":784},[783],[580,1213,1215],{"className":1214},[788,789,790,791],[580,1216,1218],{"className":1217},[623,791],[580,1219,907],{"className":1220},[623,791],[580,1222,657],{"className":1223},[724],[580,1225,1097],{"className":1226},[623],[580,1228,663],{"className":1229},[731],[580,1231],{"className":1232,"style":736},[735],[580,1234,666],{"className":1235},[740],[580,1237],{"className":1238,"style":736},[735],[580,1240,1242,1245,1248,1251,1254],{"className":1241},[614],[580,1243],{"className":1244,"style":859},[618],[580,1246,918],{"className":1247},[623],[580,1249],{"className":1250,"style":798},[735],[580,1252,680],{"className":1253},[802],[580,1255],{"className":1256,"style":798},[735],[580,1258,1260,1263,1266,1269,1272],{"className":1259},[614],[580,1261],{"className":1262,"style":859},[618],[580,1264,677],{"className":1265},[623],[580,1267],{"className":1268,"style":798},[735],[580,1270,692],{"className":1271},[802],[580,1273],{"className":1274,"style":798},[735],[580,1276,1278,1281,1284,1287,1290],{"className":1277},[614],[580,1279],{"className":1280,"style":619},[618],[580,1282,695],{"className":1283},[623],[580,1285],{"className":1286,"style":736},[735],[580,1288,666],{"className":1289},[740],[580,1291],{"className":1292,"style":736},[735],[580,1294,1296,1299],{"className":1295},[614],[580,1297],{"className":1298,"style":619},[618],[580,1300,1176],{"className":1301},[623],[559,1303,1305],{"id":1304},"typische-fehler","Typische Fehler",[1307,1308,1309,1489,1638],"ul",{},[1310,1311,1312,1313,1459,1460,1488],"li",{},"Die Konstante stehen lassen: ",[580,1314,1316,1352],{"className":1315},[583],[580,1317,1319],{"className":1318},[587],[589,1320,1321],{"xmlns":591},[593,1322,1323,1349],{},[596,1324,1325,1327,1329,1331,1333,1335,1341,1343,1345,1347],{},[654,1326,657],{"stretchy":656},[599,1328,695],{},[650,1330,660],{},[654,1332,680],{},[599,1334,702],{},[671,1336,1337,1339],{},[654,1338,663],{"stretchy":656},[654,1340,907],{"mathvariant":905,"lspace":906,"rspace":906},[654,1342,666],{},[599,1344,695],{},[654,1346,680],{},[599,1348,702],{},[603,1350,1351],{"encoding":605},"(7x - 5)' = 7 - 5",[580,1353,1355,1379,1432,1450],{"className":1354,"ariaHidden":610},[609],[580,1356,1358,1361,1364,1367,1370,1373,1376],{"className":1357},[614],[580,1359],{"className":1360,"style":715},[618],[580,1362,657],{"className":1363},[724],[580,1365,695],{"className":1366},[623],[580,1368,660],{"className":1369},[623,719],[580,1371],{"className":1372,"style":798},[735],[580,1374,680],{"className":1375},[802],[580,1377],{"className":1378,"style":798},[735],[580,1380,1382,1386,1389,1423,1426,1429],{"className":1381},[614],[580,1383],{"className":1384,"style":1385},[618],"height:1.0019em;vertical-align:-0.25em;",[580,1387,702],{"className":1388},[623],[580,1390,1392,1395],{"className":1391},[731],[580,1393,663],{"className":1394},[731],[580,1396,1398],{"className":1397},[763],[580,1399,1401],{"className":1400},[767],[580,1402,1404],{"className":1403},[771],[580,1405,1408],{"className":1406,"style":1407},[775],"height:0.7519em;",[580,1409,1411,1414],{"style":1410},"top:-3.063em;margin-right:0.05em;",[580,1412],{"className":1413,"style":784},[783],[580,1415,1417],{"className":1416},[788,789,790,791],[580,1418,1420],{"className":1419},[623,791],[580,1421,907],{"className":1422},[623,791],[580,1424],{"className":1425,"style":736},[735],[580,1427,666],{"className":1428},[740],[580,1430],{"className":1431,"style":736},[735],[580,1433,1435,1438,1441,1444,1447],{"className":1434},[614],[580,1436],{"className":1437,"style":859},[618],[580,1439,695],{"className":1440},[623],[580,1442],{"className":1443,"style":798},[735],[580,1445,680],{"className":1446},[802],[580,1448],{"className":1449,"style":798},[735],[580,1451,1453,1456],{"className":1452},[614],[580,1454],{"className":1455,"style":619},[618],[580,1457,702],{"className":1458},[623]," ist falsch, richtig ist ",[580,1461,1463,1476],{"className":1462},[583],[580,1464,1466],{"className":1465},[587],[589,1467,1468],{"xmlns":591},[593,1469,1470,1474],{},[596,1471,1472],{},[599,1473,695],{},[603,1475,695],{"encoding":605},[580,1477,1479],{"className":1478,"ariaHidden":610},[609],[580,1480,1482,1485],{"className":1481},[614],[580,1483],{"className":1484,"style":619},[618],[580,1486,695],{"className":1487},[623],".",[1310,1490,1491,1492,1563,1564,1603,1604,1488],{},"Das Vorzeichen eines Summanden verlieren: Aus ",[580,1493,1495,1517],{"className":1494},[583],[580,1496,1498],{"className":1497},[587],[589,1499,1500],{"xmlns":591},[593,1501,1502,1514],{},[596,1503,1504,1506,1508],{},[654,1505,680],{},[599,1507,683],{},[671,1509,1510,1512],{},[650,1511,660],{},[599,1513,683],{},[603,1515,1516],{"encoding":605},"-2x^2",[580,1518,1520],{"className":1519,"ariaHidden":610},[609],[580,1521,1523,1527,1530,1533],{"className":1522},[614],[580,1524],{"className":1525,"style":1526},[618],"height:0.8974em;vertical-align:-0.0833em;",[580,1528,680],{"className":1529},[623],[580,1531,683],{"className":1532},[623],[580,1534,1536,1539],{"className":1535},[623],[580,1537,660],{"className":1538},[623,719],[580,1540,1542],{"className":1541},[763],[580,1543,1545],{"className":1544},[767],[580,1546,1548],{"className":1547},[771],[580,1549,1552],{"className":1550,"style":1551},[775],"height:0.8141em;",[580,1553,1554,1557],{"style":1410},[580,1555],{"className":1556,"style":784},[783],[580,1558,1560],{"className":1559},[788,789,790,791],[580,1561,683],{"className":1562},[623,791]," wird ",[580,1565,1567,1585],{"className":1566},[583],[580,1568,1570],{"className":1569},[587],[589,1571,1572],{"xmlns":591},[593,1573,1574,1582],{},[596,1575,1576,1578,1580],{},[654,1577,680],{},[599,1579,677],{},[650,1581,660],{},[603,1583,1584],{"encoding":605},"-4x",[580,1586,1588],{"className":1587,"ariaHidden":610},[609],[580,1589,1591,1594,1597,1600],{"className":1590},[614],[580,1592],{"className":1593,"style":859},[618],[580,1595,680],{"className":1596},[623],[580,1598,677],{"className":1599},[623],[580,1601,660],{"className":1602},[623,719],", nicht ",[580,1605,1607,1623],{"className":1606},[583],[580,1608,1610],{"className":1609},[587],[589,1611,1612],{"xmlns":591},[593,1613,1614,1620],{},[596,1615,1616,1618],{},[599,1617,677],{},[650,1619,660],{},[603,1621,1622],{"encoding":605},"4x",[580,1624,1626],{"className":1625,"ariaHidden":610},[609],[580,1627,1629,1632,1635],{"className":1628},[614],[580,1630],{"className":1631,"style":619},[618],[580,1633,677],{"className":1634},[623],[580,1636,660],{"className":1637},[623,719],[1310,1639,1640,1641,1841],{},"Die Regel auf Produkte übertragen: ",[580,1642,1644,1696],{"className":1643},[583],[580,1645,1647],{"className":1646},[587],[589,1648,1649],{"xmlns":591},[593,1650,1651,1693],{},[596,1652,1653,1655,1661,1664,1667,1670,1672,1678,1680,1682,1684,1686,1689,1691],{},[654,1654,657],{"stretchy":656},[671,1656,1657,1659],{},[650,1658,660],{},[599,1660,683],{},[654,1662,1663],{},"⋅",[650,1665,1666],{},"sin",[654,1668,1669],{},"⁡",[650,1671,660],{},[671,1673,1674,1676],{},[654,1675,663],{"stretchy":656},[654,1677,907],{"mathvariant":905,"lspace":906,"rspace":906},[654,1679,666],{},[599,1681,683],{},[650,1683,660],{},[654,1685,1663],{},[650,1687,1688],{},"cos",[654,1690,1669],{},[650,1692,660],{},[603,1694,1695],{"encoding":605},"(x^2 \\cdot \\sin x)' = 2x \\cdot \\cos x",[580,1697,1699,1747,1805,1826],{"className":1698,"ariaHidden":610},[609],[580,1700,1702,1706,1709,1738,1741,1744],{"className":1701},[614],[580,1703],{"className":1704,"style":1705},[618],"height:1.0641em;vertical-align:-0.25em;",[580,1707,657],{"className":1708},[724],[580,1710,1712,1715],{"className":1711},[623],[580,1713,660],{"className":1714},[623,719],[580,1716,1718],{"className":1717},[763],[580,1719,1721],{"className":1720},[767],[580,1722,1724],{"className":1723},[771],[580,1725,1727],{"className":1726,"style":1551},[775],[580,1728,1729,1732],{"style":1410},[580,1730],{"className":1731,"style":784},[783],[580,1733,1735],{"className":1734},[788,789,790,791],[580,1736,683],{"className":1737},[623,791],[580,1739],{"className":1740,"style":798},[735],[580,1742,1663],{"className":1743},[802],[580,1745],{"className":1746,"style":798},[735],[580,1748,1750,1753,1757,1761,1764,1796,1799,1802],{"className":1749},[614],[580,1751],{"className":1752,"style":1385},[618],[580,1754,1666],{"className":1755},[1756],"mop",[580,1758],{"className":1759,"style":1760},[735],"margin-right:0.1667em;",[580,1762,660],{"className":1763},[623,719],[580,1765,1767,1770],{"className":1766},[731],[580,1768,663],{"className":1769},[731],[580,1771,1773],{"className":1772},[763],[580,1774,1776],{"className":1775},[767],[580,1777,1779],{"className":1778},[771],[580,1780,1782],{"className":1781,"style":1407},[775],[580,1783,1784,1787],{"style":1410},[580,1785],{"className":1786,"style":784},[783],[580,1788,1790],{"className":1789},[788,789,790,791],[580,1791,1793],{"className":1792},[623,791],[580,1794,907],{"className":1795},[623,791],[580,1797],{"className":1798,"style":736},[735],[580,1800,666],{"className":1801},[740],[580,1803],{"className":1804,"style":736},[735],[580,1806,1808,1811,1814,1817,1820,1823],{"className":1807},[614],[580,1809],{"className":1810,"style":619},[618],[580,1812,683],{"className":1813},[623],[580,1815,660],{"className":1816},[623,719],[580,1818],{"className":1819,"style":798},[735],[580,1821,1663],{"className":1822},[802],[580,1824],{"className":1825,"style":798},[735],[580,1827,1829,1832,1835,1838],{"className":1828},[614],[580,1830],{"className":1831,"style":1110},[618],[580,1833,1688],{"className":1834},[1756],[580,1836],{"className":1837,"style":1760},[735],[580,1839,660],{"className":1840},[623,719]," ist falsch. Hier gilt die Produktregel.",{"title":1843,"searchDepth":1844,"depth":1844,"links":1845},"",2,[1846,1847,1848],{"id":561,"depth":1844,"text":562},{"id":630,"depth":1844,"text":631},{"id":1304,"depth":1844,"text":1305},[1850,1852,1854],{"lhs":1851,"rhs":601},"round(((x+1e-5)^3 + sin(x+1e-5) - (x-1e-5)^3 - sin(x-1e-5))\u002F(2e-5) - (3*x^2 + cos(x)), 6)",{"lhs":1853,"rhs":601},"round((3*(x+1e-5)^4 - 2*(x+1e-5)^2 + 7*(x+1e-5) - 5 - (3*(x-1e-5)^4 - 2*(x-1e-5)^2 + 7*(x-1e-5) - 5))\u002F(2e-5) - (12*x^3 - 4*x + 7), 6)",{"lhs":1855,"rhs":1176},"12*1^3 - 4*1 + 7","u, v \\text{ differenzierbar}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>u\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>v\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">u, v\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:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">u\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">v\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">differenzierbar\u003C\u002Fspan>",null,"md","sum-rule","f(x) = u(x) + v(x) \\;\\Rightarrow\\; f'(x) = u'(x) + v'(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>\u003Cmi>u\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>v\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\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>\u003Cmsup>\u003Cmi>u\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>\u003Cmsup>\u003Cmi>v\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>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f(x) = u(x) + v(x) \\;\\Rightarrow\\; f'(x) = u'(x) + v'(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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" 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