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f(x_1))",[571,1060,1062,1160],{"className":1061,"ariaHidden":607},[631],[571,1063,1065,1068,1108,1111,1151,1154,1157],{"className":1064},[635],[571,1066],{"className":1067,"style":640},[639],[571,1069,1071,1074],{"className":1070},[648],[571,1072,817],{"className":1073,"style":866},[648,652],[571,1075,1077],{"className":1076},[656],[571,1078,1080,1100],{"className":1079},[660,661],[571,1081,1083,1097],{"className":1082},[665],[571,1084,1086],{"className":1085,"style":670},[669],[571,1087,1088,1091],{"style":881},[571,1089],{"className":1090,"style":678},[677],[571,1092,1094],{"className":1093},[682,683,684,685],[571,1095,619],{"className":1096},[648,685],[571,1098,693],{"className":1099},[692],[571,1101,1103],{"className":1102},[665],[571,1104,1106],{"className":1105,"style":700},[669],[571,1107],{},[571,1109,822],{"className":1110},[644],[571,1112,1114,1117],{"className":1113},[648],[571,1115,600],{"className":1116},[648,652],[571,1118,1120],{"className":1119},[656],[571,1121,1123,1143],{"className":1122},[660,661],[571,1124,1126,1140],{"className":1125},[665],[571,1127,1129],{"className":1128,"style":670},[669],[571,1130,1131,1134],{"style":673},[571,1132],{"className":1133,"style":678},[677],[571,1135,1137],{"className":1136},[682,683,684,685],[571,1138,619],{"className":1139},[648,685],[571,1141,693],{"className":1142},[692],[571,1144,1146],{"className":1145},[665],[571,1147,1149],{"className":1148,"style":700},[669],[571,1150],{},[571,1152],{"className":1153,"style":948},[710],[571,1155,831],{"className":1156},[952],[571,1158],{"className":1159,"style":948},[710],[571,1161,1163,1166,1169,1172,1212],{"className":1162},[635],[571,1164],{"className":1165,"style":640},[639],[571,1167,834],{"className":1168,"style":965},[648,652],[571,1170,822],{"className":1171},[644],[571,1173,1175,1178],{"className":1174},[648],[571,1176,600],{"className":1177},[648,652],[571,1179,1181],{"className":1180},[656],[571,1182,1184,1204],{"className":1183},[660,661],[571,1185,1187,1201],{"className":1186},[665],[571,1188,1190],{"className":1189,"style":670},[669],[571,1191,1192,1195],{"style":673},[571,1193],{"className":1194,"style":678},[677],[571,1196,1198],{"className":1197},[682,683,684,685],[571,1199,619],{"className":1200},[648,685],[571,1202,693],{"className":1203},[692],[571,1205,1207],{"className":1206},[665],[571,1208,1210],{"className":1209,"style":700},[669],[571,1211],{},[571,1213,1012],{"className":1214},[758],". Wie sich die Funktion zwischen den beiden Stellen verhält, spielt dabei keine Rolle.",[563,1217,1218,1219,1382],{},"Häufig schreibt man ",[571,1220,1222,1255],{"className":1221},[574],[571,1223,1225],{"className":1224},[578],[580,1226,1227],{"xmlns":582},[584,1228,1229,1252],{},[587,1230,1231,1237,1240,1246,1249],{},[595,1232,1233,1235],{},[598,1234,600],{},[602,1236,619],{},[590,1238,1239],{},"=",[595,1241,1242,1244],{},[598,1243,600],{},[602,1245,604],{},[590,1247,1248],{},"+",[598,1250,1251],{},"h",[624,1253,1254],{"encoding":626},"x_1 = x_0 + h",[571,1256,1258,1314,1372],{"className":1257,"ariaHidden":607},[631],[571,1259,1261,1265,1305,1308,1311],{"className":1260},[635],[571,1262],{"className":1263,"style":1264},[639],"height:0.5806em;vertical-align:-0.15em;",[571,1266,1268,1271],{"className":1267},[648],[571,1269,600],{"className":1270},[648,652],[571,1272,1274],{"className":1273},[656],[571,1275,1277,1297],{"className":1276},[660,661],[571,1278,1280,1294],{"className":1279},[665],[571,1281,1283],{"className":1282,"style":670},[669],[571,1284,1285,1288],{"style":673},[571,1286],{"className":1287,"style":678},[677],[571,1289,1291],{"className":1290},[682,683,684,685],[571,1292,619],{"className":1293},[648,685],[571,1295,693],{"className":1296},[692],[571,1298,1300],{"className":1299},[665],[571,1301,1303],{"className":1302,"style":700},[669],[571,1304],{},[571,1306],{"className":1307,"style":948},[710],[571,1309,1239],{"className":1310},[952],[571,1312],{"className":1313,"style":948},[710],[571,1315,1317,1321,1361,1365,1369],{"className":1316},[635],[571,1318],{"className":1319,"style":1320},[639],"height:0.7333em;vertical-align:-0.15em;",[571,1322,1324,1327],{"className":1323},[648],[571,1325,600],{"className":1326},[648,652],[571,1328,1330],{"className":1329},[656],[571,1331,1333,1353],{"className":1332},[660,661],[571,1334,1336,1350],{"className":1335},[665],[571,1337,1339],{"className":1338,"style":670},[669],[571,1340,1341,1344],{"style":673},[571,1342],{"className":1343,"style":678},[677],[571,1345,1347],{"className":1346},[682,683,684,685],[571,1348,604],{"className":1349},[648,685],[571,1351,693],{"className":1352},[692],[571,1354,1356],{"className":1355},[665],[571,1357,1359],{"className":1358,"style":700},[669],[571,1360],{},[571,1362],{"className":1363,"style":1364},[710],"margin-right:0.2222em;",[571,1366,1248],{"className":1367},[1368],"mbin",[571,1370],{"className":1371,"style":1364},[710],[571,1373,1375,1379],{"className":1374},[635],[571,1376],{"className":1377,"style":1378},[639],"height:0.6944em;",[571,1380,1251],{"className":1381},[648,652],". Dann lautet der Differenzenquotient",[571,1384,1387],{"className":1385},[1386],"katex-display",[571,1388,1390,1456],{"className":1389},[574],[571,1391,1393],{"className":1392},[578],[580,1394,1396],{"xmlns":582,"display":1395},"block",[584,1397,1398,1453],{},[587,1399,1400,1438,1441,1444,1446,1450],{},[1401,1402,1403,1436],"mfrac",{},[587,1404,1405,1407,1409,1415,1417,1419,1421,1424,1426,1428,1434],{},[598,1406,834],{},[590,1408,822],{"stretchy":592},[595,1410,1411,1413],{},[598,1412,600],{},[602,1414,604],{},[590,1416,1248],{},[598,1418,1251],{},[590,1420,845],{"stretchy":592},[590,1422,1423],{},"−",[598,1425,834],{},[590,1427,822],{"stretchy":592},[595,1429,1430,1432],{},[598,1431,600],{},[602,1433,604],{},[590,1435,845],{"stretchy":592},[598,1437,1251],{},[590,1439,1440],{"separator":607},",",[710,1442],{"width":1443},"1em",[598,1445,1251],{},[590,1447,1449],{"mathvariant":1448},"normal","≠",[602,1451,1452],{},"0.",[624,1454,1455],{"encoding":626},"\\frac{f(x_0 + h) - f(x_0)}{h}, \\quad h \\neq 0.",[571,1457,1459,1716],{"className":1458,"ariaHidden":607},[631],[571,1460,1462,1466,1653,1656,1660,1663,1666,1669,1713],{"className":1461},[635],[571,1463],{"className":1464,"style":1465},[639],"height:2.113em;vertical-align:-0.686em;",[571,1467,1469,1473,1650],{"className":1468},[648],[571,1470],{"className":1471},[644,1472],"nulldelimiter",[571,1474,1476],{"className":1475},[1401],[571,1477,1479,1641],{"className":1478},[660,661],[571,1480,1482,1638],{"className":1481},[665],[571,1483,1486,1499,1510],{"className":1484,"style":1485},[669],"height:1.427em;",[571,1487,1489,1493],{"style":1488},"top:-2.314em;",[571,1490],{"className":1491,"style":1492},[677],"height:3em;",[571,1494,1496],{"className":1495},[648],[571,1497,1251],{"className":1498},[648,652],[571,1500,1502,1505],{"style":1501},"top:-3.23em;",[571,1503],{"className":1504,"style":1492},[677],[571,1506],{"className":1507,"style":1509},[1508],"frac-line","border-bottom-width:0.04em;",[571,1511,1513,1516],{"style":1512},"top:-3.677em;",[571,1514],{"className":1515,"style":1492},[677],[571,1517,1519,1522,1525,1565,1568,1571,1574,1577,1580,1583,1586,1589,1592,1595,1635],{"className":1518},[648],[571,1520,834],{"className":1521,"style":965},[648,652],[571,1523,822],{"className":1524},[644],[571,1526,1528,1531],{"className":1527},[648],[571,1529,600],{"className":1530},[648,652],[571,1532,1534],{"className":1533},[656],[571,1535,1537,1557],{"className":1536},[660,661],[571,1538,1540,1554],{"className":1539},[665],[571,1541,1543],{"className":1542,"style":670},[669],[571,1544,1545,1548],{"style":673},[571,1546],{"className":1547,"style":678},[677],[571,1549,1551],{"className":1550},[682,683,684,685],[571,1552,604],{"className":1553},[648,685],[571,1555,693],{"className":1556},[692],[571,1558,1560],{"className":1559},[665],[571,1561,1563],{"className":1562,"style":700},[669],[571,1564],{},[571,1566],{"className":1567,"style":1364},[710],[571,1569,1248],{"className":1570},[1368],[571,1572],{"className":1573,"style":1364},[710],[571,1575,1251],{"className":1576},[648,652],[571,1578,845],{"className":1579},[758],[571,1581],{"className":1582,"style":1364},[710],[571,1584,1423],{"className":1585},[1368],[571,1587],{"className":1588,"style":1364},[710],[571,1590,834],{"className":1591,"style":965},[648,652],[571,1593,822],{"className":1594},[644],[571,1596,1598,1601],{"className":1597},[648],[571,1599,600],{"className":1600},[648,652],[571,1602,1604],{"className":1603},[656],[571,1605,1607,1627],{"className":1606},[660,661],[571,1608,1610,1624],{"className":1609},[665],[571,1611,1613],{"className":1612,"style":670},[669],[571,1614,1615,1618],{"style":673},[571,1616],{"className":1617,"style":678},[677],[571,1619,1621],{"className":1620},[682,683,684,685],[571,1622,604],{"className":1623},[648,685],[571,1625,693],{"className":1626},[692],[571,1628,1630],{"className":1629},[665],[571,1631,1633],{"className":1632,"style":700},[669],[571,1634],{},[571,1636,845],{"className":1637},[758],[571,1639,693],{"className":1640},[692],[571,1642,1644],{"className":1643},[665],[571,1645,1648],{"className":1646,"style":1647},[669],"height:0.686em;",[571,1649],{},[571,1651],{"className":1652},[758,1472],[571,1654,1440],{"className":1655},[706],[571,1657],{"className":1658,"style":1659},[710],"margin-right:1em;",[571,1661],{"className":1662,"style":711},[710],[571,1664,1251],{"className":1665},[648,652],[571,1667],{"className":1668,"style":948},[710],[571,1670,1672,1706,1710],{"className":1671},[952],[571,1673,1675],{"className":1674},[952],[571,1676,1679],{"className":1677},[648,1678],"vbox",[571,1680,1683],{"className":1681},[1682],"thinbox",[571,1684,1687,1691,1702],{"className":1685},[1686],"rlap",[571,1688],{"className":1689,"style":1690},[639],"height:0.8889em;vertical-align:-0.1944em;",[571,1692,1695],{"className":1693},[1694],"inner",[571,1696,1698],{"className":1697},[648],[571,1699,1701],{"className":1700},[952],"",[571,1703],{"className":1704},[1705],"fix",[571,1707],{"className":1708},[710,1709],"nobreak",[571,1711,1239],{"className":1712},[952],[571,1714],{"className":1715,"style":948},[710],[571,1717,1719,1723],{"className":1718},[635],[571,1720],{"className":1721,"style":1722},[639],"height:0.6444em;",[571,1724,1452],{"className":1725},[648],[563,1727,1728,1729,1757,1758,1761],{},"Lässt man ",[571,1730,1732,1745],{"className":1731},[574],[571,1733,1735],{"className":1734},[578],[580,1736,1737],{"xmlns":582},[584,1738,1739,1743],{},[587,1740,1741],{},[598,1742,1251],{},[624,1744,1251],{"encoding":626},[571,1746,1748],{"className":1747,"ariaHidden":607},[631],[571,1749,1751,1754],{"className":1750},[635],[571,1752],{"className":1753,"style":1378},[639],[571,1755,1251],{"className":1756},[648,652]," gegen null gehen, erhält man den ",[567,1759,1760],{},"Differentialquotienten",", also die Ableitung.",[563,1763,1764,1765,1796,1797,1825],{},"Die Einheit der mittleren Änderungsrate ist „Einheit von ",[571,1766,1768,1782],{"className":1767},[574],[571,1769,1771],{"className":1770},[578],[580,1772,1773],{"xmlns":582},[584,1774,1775,1780],{},[587,1776,1777],{},[598,1778,1779],{},"y",[624,1781,1779],{"encoding":626},[571,1783,1785],{"className":1784,"ariaHidden":607},[631],[571,1786,1788,1792],{"className":1787},[635],[571,1789],{"className":1790,"style":1791},[639],"height:0.625em;vertical-align:-0.1944em;",[571,1793,1779],{"className":1794,"style":1795},[648,652],"margin-right:0.0359em;"," pro Einheit von ",[571,1798,1800,1813],{"className":1799},[574],[571,1801,1803],{"className":1802},[578],[580,1804,1805],{"xmlns":582},[584,1806,1807,1811],{},[587,1808,1809],{},[598,1810,600],{},[624,1812,600],{"encoding":626},[571,1814,1816],{"className":1815,"ariaHidden":607},[631],[571,1817,1819,1822],{"className":1818},[635],[571,1820],{"className":1821,"style":789},[639],[571,1823,600],{"className":1824},[648,652],"“, z.B. Meter pro Sekunde.",[558,1827,1829],{"id":1828},"beispiele","Beispiele",[563,1831,1832,1833,1933,1934,1992],{},"Für ",[571,1834,1836,1866],{"className":1835},[574],[571,1837,1839],{"className":1838},[578],[580,1840,1841],{"xmlns":582},[584,1842,1843,1863],{},[587,1844,1845,1847,1849,1851,1853,1855],{},[598,1846,834],{},[590,1848,822],{"stretchy":592},[598,1850,600],{},[590,1852,845],{"stretchy":592},[590,1854,1239],{},[1856,1857,1858,1860],"msup",{},[598,1859,600],{},[602,1861,1862],{},"2",[624,1864,1865],{"encoding":626},"f(x) = x^2",[571,1867,1869,1896],{"className":1868,"ariaHidden":607},[631],[571,1870,1872,1875,1878,1881,1884,1887,1890,1893],{"className":1871},[635],[571,1873],{"className":1874,"style":640},[639],[571,1876,834],{"className":1877,"style":965},[648,652],[571,1879,822],{"className":1880},[644],[571,1882,600],{"className":1883},[648,652],[571,1885,845],{"className":1886},[758],[571,1888],{"className":1889,"style":948},[710],[571,1891,1239],{"className":1892},[952],[571,1894],{"className":1895,"style":948},[710],[571,1897,1899,1903],{"className":1898},[635],[571,1900],{"className":1901,"style":1902},[639],"height:0.8141em;",[571,1904,1906,1909],{"className":1905},[648],[571,1907,600],{"className":1908},[648,652],[571,1910,1912],{"className":1911},[656],[571,1913,1915],{"className":1914},[660],[571,1916,1918],{"className":1917},[665],[571,1919,1921],{"className":1920,"style":1902},[669],[571,1922,1924,1927],{"style":1923},"top:-3.063em;margin-right:0.05em;",[571,1925],{"className":1926,"style":678},[677],[571,1928,1930],{"className":1929},[682,683,684,685],[571,1931,1862],{"className":1932},[648,685]," auf dem Intervall ",[571,1935,1937,1962],{"className":1936},[574],[571,1938,1940],{"className":1939},[578],[580,1941,1942],{"xmlns":582},[584,1943,1944,1959],{},[587,1945,1946,1948,1950,1952,1954,1957],{},[590,1947,593],{"stretchy":592},[602,1949,619],{},[590,1951,608],{"separator":607},[610,1953,612],{},[602,1955,1956],{},"3",[590,1958,622],{"stretchy":592},[624,1960,1961],{"encoding":626},"[1;\\, 3]",[571,1963,1965],{"className":1964,"ariaHidden":607},[631],[571,1966,1968,1971,1974,1977,1980,1983,1986,1989],{"className":1967},[635],[571,1969],{"className":1970,"style":640},[639],[571,1972,593],{"className":1973},[644],[571,1975,619],{"className":1976},[648],[571,1978,608],{"className":1979},[706],[571,1981],{"className":1982,"style":711},[710],[571,1984],{"className":1985,"style":711},[710],[571,1987,1956],{"className":1988},[648],[571,1990,622],{"className":1991},[758],":",[571,1994,1996],{"className":1995},[1386],[571,1997,1999,2061],{"className":1998},[574],[571,2000,2002],{"className":2001},[578],[580,2003,2004],{"xmlns":582,"display":1395},[584,2005,2006,2058],{},[587,2007,2008,2038,2040,2053,2055],{},[1401,2009,2010,2030],{},[587,2011,2012,2014,2016,2018,2020,2022,2024,2026,2028],{},[598,2013,834],{},[590,2015,822],{"stretchy":592},[602,2017,1956],{},[590,2019,845],{"stretchy":592},[590,2021,1423],{},[598,2023,834],{},[590,2025,822],{"stretchy":592},[602,2027,619],{},[590,2029,845],{"stretchy":592},[587,2031,2032,2034,2036],{},[602,2033,1956],{},[590,2035,1423],{},[602,2037,619],{},[590,2039,1239],{},[1401,2041,2042,2051],{},[587,2043,2044,2047,2049],{},[602,2045,2046],{},"9",[590,2048,1423],{},[602,2050,619],{},[602,2052,1862],{},[590,2054,1239],{},[602,2056,2057],{},"4",[624,2059,2060],{"encoding":626},"\\frac{f(3) - f(1)}{3 - 1} = \\frac{9 - 1}{2} = 4",[571,2062,2064,2185,2276],{"className":2063,"ariaHidden":607},[631],[571,2065,2067,2071,2176,2179,2182],{"className":2066},[635],[571,2068],{"className":2069,"style":2070},[639],"height:2.1963em;vertical-align:-0.7693em;",[571,2072,2074,2077,2173],{"className":2073},[648],[571,2075],{"className":2076},[644,1472],[571,2078,2080],{"className":2079},[1401],[571,2081,2083,2164],{"className":2082},[660,661],[571,2084,2086,2161],{"className":2085},[665],[571,2087,2089,2112,2120],{"className":2088,"style":1485},[669],[571,2090,2091,2094],{"style":1488},[571,2092],{"className":2093,"style":1492},[677],[571,2095,2097,2100,2103,2106,2109],{"className":2096},[648],[571,2098,1956],{"className":2099},[648],[571,2101],{"className":2102,"style":1364},[710],[571,2104,1423],{"className":2105},[1368],[571,2107],{"className":2108,"style":1364},[710],[571,2110,619],{"className":2111},[648],[571,2113,2114,2117],{"style":1501},[571,2115],{"className":2116,"style":1492},[677],[571,2118],{"className":2119,"style":1509},[1508],[571,2121,2122,2125],{"style":1512},[571,2123],{"className":2124,"style":1492},[677],[571,2126,2128,2131,2134,2137,2140,2143,2146,2149,2152,2155,2158],{"className":2127},[648],[571,2129,834],{"className":2130,"style":965},[648,652],[571,2132,822],{"className":2133},[644],[571,2135,1956],{"className":2136},[648],[571,2138,845],{"className":2139},[758],[571,2141],{"className":2142,"style":1364},[710],[571,2144,1423],{"className":2145},[1368],[571,2147],{"className":2148,"style":1364},[710],[571,2150,834],{"className":2151,"style":965},[648,652],[571,2153,822],{"className":2154},[644],[571,2156,619],{"className":2157},[648],[571,2159,845],{"className":2160},[758],[571,2162,693],{"className":2163},[692],[571,2165,2167],{"className":2166},[665],[571,2168,2171],{"className":2169,"style":2170},[669],"height:0.7693em;",[571,2172],{},[571,2174],{"className":2175},[758,1472],[571,2177],{"className":2178,"style":948},[710],[571,2180,1239],{"className":2181},[952],[571,2183],{"className":2184,"style":948},[710],[571,2186,2188,2192,2267,2270,2273],{"className":2187},[635],[571,2189],{"className":2190,"style":2191},[639],"height:2.0074em;vertical-align:-0.686em;",[571,2193,2195,2198,2264],{"className":2194},[648],[571,2196],{"className":2197},[644,1472],[571,2199,2201],{"className":2200},[1401],[571,2202,2204,2256],{"className":2203},[660,661],[571,2205,2207,2253],{"className":2206},[665],[571,2208,2211,2222,2230],{"className":2209,"style":2210},[669],"height:1.3214em;",[571,2212,2213,2216],{"style":1488},[571,2214],{"className":2215,"style":1492},[677],[571,2217,2219],{"className":2218},[648],[571,2220,1862],{"className":2221},[648],[571,2223,2224,2227],{"style":1501},[571,2225],{"className":2226,"style":1492},[677],[571,2228],{"className":2229,"style":1509},[1508],[571,2231,2232,2235],{"style":1512},[571,2233],{"className":2234,"style":1492},[677],[571,2236,2238,2241,2244,2247,2250],{"className":2237},[648],[571,2239,2046],{"className":2240},[648],[571,2242],{"className":2243,"style":1364},[710],[571,2245,1423],{"className":2246},[1368],[571,2248],{"className":2249,"style":1364},[710],[571,2251,619],{"className":2252},[648],[571,2254,693],{"className":2255},[692],[571,2257,2259],{"className":2258},[665],[571,2260,2262],{"className":2261,"style":1647},[669],[571,2263],{},[571,2265],{"className":2266},[758,1472],[571,2268],{"className":2269,"style":948},[710],[571,2271,1239],{"className":2272},[952],[571,2274],{"className":2275,"style":948},[710],[571,2277,2279,2282],{"className":2278},[635],[571,2280],{"className":2281,"style":1722},[639],[571,2283,2057],{"className":2284},[648],[563,2286,2287,2288,2318,2319,2422,2423,2608,2609,1013,2673,2737],{},"Ein fallender Stein legt in den ersten ",[571,2289,2291,2305],{"className":2290},[574],[571,2292,2294],{"className":2293},[578],[580,2295,2296],{"xmlns":582},[584,2297,2298,2303],{},[587,2299,2300],{},[598,2301,2302],{},"t",[624,2304,2302],{"encoding":626},[571,2306,2308],{"className":2307,"ariaHidden":607},[631],[571,2309,2311,2315],{"className":2310},[635],[571,2312],{"className":2313,"style":2314},[639],"height:0.6151em;",[571,2316,2302],{"className":2317},[648,652]," Sekunden ungefähr ",[571,2320,2322,2354],{"className":2321},[574],[571,2323,2325],{"className":2324},[578],[580,2326,2327],{"xmlns":582},[584,2328,2329,2351],{},[587,2330,2331,2334,2336,2338,2340,2342,2345],{},[598,2332,2333],{},"s",[590,2335,822],{"stretchy":592},[598,2337,2302],{},[590,2339,845],{"stretchy":592},[590,2341,1239],{},[602,2343,2344],{},"5",[1856,2346,2347,2349],{},[598,2348,2302],{},[602,2350,1862],{},[624,2352,2353],{"encoding":626},"s(t) = 5t^2",[571,2355,2357,2384],{"className":2356,"ariaHidden":607},[631],[571,2358,2360,2363,2366,2369,2372,2375,2378,2381],{"className":2359},[635],[571,2361],{"className":2362,"style":640},[639],[571,2364,2333],{"className":2365},[648,652],[571,2367,822],{"className":2368},[644],[571,2370,2302],{"className":2371},[648,652],[571,2373,845],{"className":2374},[758],[571,2376],{"className":2377,"style":948},[710],[571,2379,1239],{"className":2380},[952],[571,2382],{"className":2383,"style":948},[710],[571,2385,2387,2390,2393],{"className":2386},[635],[571,2388],{"className":2389,"style":1902},[639],[571,2391,2344],{"className":2392},[648],[571,2394,2396,2399],{"className":2395},[648],[571,2397,2302],{"className":2398},[648,652],[571,2400,2402],{"className":2401},[656],[571,2403,2405],{"className":2404},[660],[571,2406,2408],{"className":2407},[665],[571,2409,2411],{"className":2410,"style":1902},[669],[571,2412,2413,2416],{"style":1923},[571,2414],{"className":2415,"style":678},[677],[571,2417,2419],{"className":2418},[682,683,684,685],[571,2420,1862],{"className":2421},[648,685]," Meter zurück (ohne Luftwiderstand und mit ",[571,2424,2426,2463],{"className":2425},[574],[571,2427,2429],{"className":2428},[578],[580,2430,2431],{"xmlns":582},[584,2432,2433,2460],{},[587,2434,2435,2438,2441,2444,2446],{},[598,2436,2437],{},"g",[590,2439,2440],{},"≈",[602,2442,2443],{},"10",[610,2445,612],{},[2447,2448,2449],"mstyle",{"scriptlevel":604,"displaystyle":592},[1401,2450,2451,2454],{},[610,2452,2453],{},"m",[1856,2455,2456,2458],{},[610,2457,2333],{},[602,2459,1862],{},[624,2461,2462],{"encoding":626},"g \\approx 10\\,\\tfrac{\\text{m}}{\\text{s}^2}",[571,2464,2466,2485],{"className":2465,"ariaHidden":607},[631],[571,2467,2469,2473,2476,2479,2482],{"className":2468},[635],[571,2470],{"className":2471,"style":2472},[639],"height:0.6776em;vertical-align:-0.1944em;",[571,2474,2437],{"className":2475,"style":1795},[648,652],[571,2477],{"className":2478,"style":948},[710],[571,2480,2440],{"className":2481},[952],[571,2483],{"className":2484,"style":948},[710],[571,2486,2488,2492,2495,2498],{"className":2487},[635],[571,2489],{"className":2490,"style":2491},[639],"height:1.0404em;vertical-align:-0.345em;",[571,2493,2443],{"className":2494},[648],[571,2496],{"className":2497,"style":711},[710],[571,2499,2501,2504,2605],{"className":2500},[648],[571,2502],{"className":2503},[644,1472],[571,2505,2507],{"className":2506},[1401],[571,2508,2510,2596],{"className":2509},[660,661],[571,2511,2513,2593],{"className":2512},[665],[571,2514,2517,2567,2575],{"className":2515,"style":2516},[669],"height:0.6954em;",[571,2518,2520,2523],{"style":2519},"top:-2.655em;",[571,2521],{"className":2522,"style":1492},[677],[571,2524,2526],{"className":2525},[682,683,684,685],[571,2527,2529],{"className":2528},[648,685],[571,2530,2532,2539],{"className":2531},[648,685],[571,2533,2536],{"className":2534},[648,2535,685],"text",[571,2537,2333],{"className":2538},[648,685],[571,2540,2542],{"className":2541},[656],[571,2543,2545],{"className":2544},[660],[571,2546,2548],{"className":2547},[665],[571,2549,2552],{"className":2550,"style":2551},[669],"height:0.7463em;",[571,2553,2555,2559],{"style":2554},"top:-2.786em;margin-right:0.0714em;",[571,2556],{"className":2557,"style":2558},[677],"height:2.5em;",[571,2560,2564],{"className":2561},[682,2562,2563,685],"reset-size3","size1",[571,2565,1862],{"className":2566},[648,685],[571,2568,2569,2572],{"style":1501},[571,2570],{"className":2571,"style":1492},[677],[571,2573],{"className":2574,"style":1509},[1508],[571,2576,2578,2581],{"style":2577},"top:-3.394em;",[571,2579],{"className":2580,"style":1492},[677],[571,2582,2584],{"className":2583},[682,683,684,685],[571,2585,2587],{"className":2586},[648,685],[571,2588,2590],{"className":2589},[648,2535,685],[571,2591,2453],{"className":2592},[648,685],[571,2594,693],{"className":2595},[692],[571,2597,2599],{"className":2598},[665],[571,2600,2603],{"className":2601,"style":2602},[669],"height:0.345em;",[571,2604],{},[571,2606],{"className":2607},[758,1472]," gerechnet). Die mittlere Geschwindigkeit zwischen ",[571,2610,2612,2634],{"className":2611},[574],[571,2613,2615],{"className":2614},[578],[580,2616,2617],{"xmlns":582},[584,2618,2619,2631],{},[587,2620,2621,2623,2625,2627,2629],{},[598,2622,2302],{},[590,2624,1239],{},[602,2626,619],{},[610,2628,612],{},[610,2630,2333],{},[624,2632,2633],{"encoding":626},"t = 1\\,\\text{s}",[571,2635,2637,2655],{"className":2636,"ariaHidden":607},[631],[571,2638,2640,2643,2646,2649,2652],{"className":2639},[635],[571,2641],{"className":2642,"style":2314},[639],[571,2644,2302],{"className":2645},[648,652],[571,2647],{"className":2648,"style":948},[710],[571,2650,1239],{"className":2651},[952],[571,2653],{"className":2654,"style":948},[710],[571,2656,2658,2661,2664,2667],{"className":2657},[635],[571,2659],{"className":2660,"style":1722},[639],[571,2662,619],{"className":2663},[648],[571,2665],{"className":2666,"style":711},[710],[571,2668,2670],{"className":2669},[648,2535],[571,2671,2333],{"className":2672},[648],[571,2674,2676,2698],{"className":2675},[574],[571,2677,2679],{"className":2678},[578],[580,2680,2681],{"xmlns":582},[584,2682,2683,2695],{},[587,2684,2685,2687,2689,2691,2693],{},[598,2686,2302],{},[590,2688,1239],{},[602,2690,1956],{},[610,2692,612],{},[610,2694,2333],{},[624,2696,2697],{"encoding":626},"t = 3\\,\\text{s}",[571,2699,2701,2719],{"className":2700,"ariaHidden":607},[631],[571,2702,2704,2707,2710,2713,2716],{"className":2703},[635],[571,2705],{"className":2706,"style":2314},[639],[571,2708,2302],{"className":2709},[648,652],[571,2711],{"className":2712,"style":948},[710],[571,2714,1239],{"className":2715},[952],[571,2717],{"className":2718,"style":948},[710],[571,2720,2722,2725,2728,2731],{"className":2721},[635],[571,2723],{"className":2724,"style":1722},[639],[571,2726,1956],{"className":2727},[648],[571,2729],{"className":2730,"style":711},[710],[571,2732,2734],{"className":2733},[648,2535],[571,2735,2333],{"className":2736},[648]," ist",[571,2739,2741],{"className":2740},[1386],[571,2742,2744,2816],{"className":2743},[574],[571,2745,2747],{"className":2746},[578],[580,2748,2749],{"xmlns":582,"display":1395},[584,2750,2751,2813],{},[587,2752,2753,2783,2785,2798,2800,2803,2805],{},[1401,2754,2755,2775],{},[587,2756,2757,2759,2761,2763,2765,2767,2769,2771,2773],{},[598,2758,2333],{},[590,2760,822],{"stretchy":592},[602,2762,1956],{},[590,2764,845],{"stretchy":592},[590,2766,1423],{},[598,2768,2333],{},[590,2770,822],{"stretchy":592},[602,2772,619],{},[590,2774,845],{"stretchy":592},[587,2776,2777,2779,2781],{},[602,2778,1956],{},[590,2780,1423],{},[602,2782,619],{},[590,2784,1239],{},[1401,2786,2787,2796],{},[587,2788,2789,2792,2794],{},[602,2790,2791],{},"45",[590,2793,1423],{},[602,2795,2344],{},[602,2797,1862],{},[590,2799,1239],{},[602,2801,2802],{},"20",[610,2804,612],{},[2447,2806,2807],{"scriptlevel":604,"displaystyle":592},[1401,2808,2809,2811],{},[610,2810,2453],{},[610,2812,2333],{},[624,2814,2815],{"encoding":626},"\\frac{s(3) - s(1)}{3 - 1} = \\frac{45 - 5}{2} = 20\\,\\tfrac{\\text{m}}{\\text{s}}",[571,2817,2819,2938,3027],{"className":2818,"ariaHidden":607},[631],[571,2820,2822,2825,2929,2932,2935],{"className":2821},[635],[571,2823],{"className":2824,"style":2070},[639],[571,2826,2828,2831,2926],{"className":2827},[648],[571,2829],{"className":2830},[644,1472],[571,2832,2834],{"className":2833},[1401],[571,2835,2837,2918],{"className":2836},[660,661],[571,2838,2840,2915],{"className":2839},[665],[571,2841,2843,2866,2874],{"className":2842,"style":1485},[669],[571,2844,2845,2848],{"style":1488},[571,2846],{"className":2847,"style":1492},[677],[571,2849,2851,2854,2857,2860,2863],{"className":2850},[648],[571,2852,1956],{"className":2853},[648],[571,2855],{"className":2856,"style":1364},[710],[571,2858,1423],{"className":2859},[1368],[571,2861],{"className":2862,"style":1364},[710],[571,2864,619],{"className":2865},[648],[571,2867,2868,2871],{"style":1501},[571,2869],{"className":2870,"style":1492},[677],[571,2872],{"className":2873,"style":1509},[1508],[571,2875,2876,2879],{"style":1512},[571,2877],{"className":2878,"style":1492},[677],[571,2880,2882,2885,2888,2891,2894,2897,2900,2903,2906,2909,2912],{"className":2881},[648],[571,2883,2333],{"className":2884},[648,652],[571,2886,822],{"className":2887},[644],[571,2889,1956],{"className":2890},[648],[571,2892,845],{"className":2893},[758],[571,2895],{"className":2896,"style":1364},[710],[571,2898,1423],{"className":2899},[1368],[571,2901],{"className":2902,"style":1364},[710],[571,2904,2333],{"className":2905},[648,652],[571,2907,822],{"className":2908},[644],[571,2910,619],{"className":2911},[648],[571,2913,845],{"className":2914},[758],[571,2916,693],{"className":2917},[692],[571,2919,2921],{"className":2920},[665],[571,2922,2924],{"className":2923,"style":2170},[669],[571,2925],{},[571,2927],{"className":2928},[758,1472],[571,2930],{"className":2931,"style":948},[710],[571,2933,1239],{"className":2934},[952],[571,2936],{"className":2937,"style":948},[710],[571,2939,2941,2944,3018,3021,3024],{"className":2940},[635],[571,2942],{"className":2943,"style":2191},[639],[571,2945,2947,2950,3015],{"className":2946},[648],[571,2948],{"className":2949},[644,1472],[571,2951,2953],{"className":2952},[1401],[571,2954,2956,3007],{"className":2955},[660,661],[571,2957,2959,3004],{"className":2958},[665],[571,2960,2962,2973,2981],{"className":2961,"style":2210},[669],[571,2963,2964,2967],{"style":1488},[571,2965],{"className":2966,"style":1492},[677],[571,2968,2970],{"className":2969},[648],[571,2971,1862],{"className":2972},[648],[571,2974,2975,2978],{"style":1501},[571,2976],{"className":2977,"style":1492},[677],[571,2979],{"className":2980,"style":1509},[1508],[571,2982,2983,2986],{"style":1512},[571,2984],{"className":2985,"style":1492},[677],[571,2987,2989,2992,2995,2998,3001],{"className":2988},[648],[571,2990,2791],{"className":2991},[648],[571,2993],{"className":2994,"style":1364},[710],[571,2996,1423],{"className":2997},[1368],[571,2999],{"className":3000,"style":1364},[710],[571,3002,2344],{"className":3003},[648],[571,3005,693],{"className":3006},[692],[571,3008,3010],{"className":3009},[665],[571,3011,3013],{"className":3012,"style":1647},[669],[571,3014],{},[571,3016],{"className":3017},[758,1472],[571,3019],{"className":3020,"style":948},[710],[571,3022,1239],{"className":3023},[952],[571,3025],{"className":3026,"style":948},[710],[571,3028,3030,3033,3036,3039],{"className":3029},[635],[571,3031],{"className":3032,"style":2491},[639],[571,3034,2802],{"className":3035},[648],[571,3037],{"className":3038,"style":711},[710],[571,3040,3042,3045,3110],{"className":3041},[648],[571,3043],{"className":3044},[644,1472],[571,3046,3048],{"className":3047},[1401],[571,3049,3051,3102],{"className":3050},[660,661],[571,3052,3054,3099],{"className":3053},[665],[571,3055,3057,3074,3082],{"className":3056,"style":2516},[669],[571,3058,3059,3062],{"style":2519},[571,3060],{"className":3061,"style":1492},[677],[571,3063,3065],{"className":3064},[682,683,684,685],[571,3066,3068],{"className":3067},[648,685],[571,3069,3071],{"className":3070},[648,2535,685],[571,3072,2333],{"className":3073},[648,685],[571,3075,3076,3079],{"style":1501},[571,3077],{"className":3078,"style":1492},[677],[571,3080],{"className":3081,"style":1509},[1508],[571,3083,3084,3087],{"style":2577},[571,3085],{"className":3086,"style":1492},[677],[571,3088,3090],{"className":3089},[682,683,684,685],[571,3091,3093],{"className":3092},[648,685],[571,3094,3096],{"className":3095},[648,2535,685],[571,3097,2453],{"className":3098},[648,685],[571,3100,693],{"className":3101},[692],[571,3103,3105],{"className":3104},[665],[571,3106,3108],{"className":3107,"style":2602},[669],[571,3109],{},[571,3111],{"className":3112},[758,1472],[558,3114,3116],{"id":3115},"typische-fehler","Typische Fehler",[3118,3119,3120,3346,3511],"ul",{},[3121,3122,3123,3124,3280,3281,3316,3317,3345],"li",{},"Die Reihenfolge nur im Zähler oder nur im Nenner tauschen. ",[571,3125,3127,3169],{"className":3126},[574],[571,3128,3130],{"className":3129},[578],[580,3131,3132],{"xmlns":582},[584,3133,3134,3166],{},[587,3135,3136],{},[1401,3137,3138,3158],{},[587,3139,3140,3142,3144,3146,3148,3150,3152,3154,3156],{},[598,3141,834],{},[590,3143,822],{"stretchy":592},[602,3145,619],{},[590,3147,845],{"stretchy":592},[590,3149,1423],{},[598,3151,834],{},[590,3153,822],{"stretchy":592},[602,3155,1956],{},[590,3157,845],{"stretchy":592},[587,3159,3160,3162,3164],{},[602,3161,1956],{},[590,3163,1423],{},[602,3165,619],{},[624,3167,3168],{"encoding":626},"\\frac{f(1) - f(3)}{3 - 1}",[571,3170,3172],{"className":3171,"ariaHidden":607},[631],[571,3173,3175,3179],{"className":3174},[635],[571,3176],{"className":3177,"style":3178},[639],"height:1.4133em;vertical-align:-0.4033em;",[571,3180,3182,3185,3277],{"className":3181},[648],[571,3183],{"className":3184},[644,1472],[571,3186,3188],{"className":3187},[1401],[571,3189,3191,3268],{"className":3190},[660,661],[571,3192,3194,3265],{"className":3193},[665],[571,3195,3198,3218,3226],{"className":3196,"style":3197},[669],"height:1.01em;",[571,3199,3200,3203],{"style":2519},[571,3201],{"className":3202,"style":1492},[677],[571,3204,3206],{"className":3205},[682,683,684,685],[571,3207,3209,3212,3215],{"className":3208},[648,685],[571,3210,1956],{"className":3211},[648,685],[571,3213,1423],{"className":3214},[1368,685],[571,3216,619],{"className":3217},[648,685],[571,3219,3220,3223],{"style":1501},[571,3221],{"className":3222,"style":1492},[677],[571,3224],{"className":3225,"style":1509},[1508],[571,3227,3229,3232],{"style":3228},"top:-3.485em;",[571,3230],{"className":3231,"style":1492},[677],[571,3233,3235],{"className":3234},[682,683,684,685],[571,3236,3238,3241,3244,3247,3250,3253,3256,3259,3262],{"className":3237},[648,685],[571,3239,834],{"className":3240,"style":965},[648,652,685],[571,3242,822],{"className":3243},[644,685],[571,3245,619],{"className":3246},[648,685],[571,3248,845],{"className":3249},[758,685],[571,3251,1423],{"className":3252},[1368,685],[571,3254,834],{"className":3255,"style":965},[648,652,685],[571,3257,822],{"className":3258},[644,685],[571,3260,1956],{"className":3261},[648,685],[571,3263,845],{"className":3264},[758,685],[571,3266,693],{"className":3267},[692],[571,3269,3271],{"className":3270},[665],[571,3272,3275],{"className":3273,"style":3274},[669],"height:0.4033em;",[571,3276],{},[571,3278],{"className":3279},[758,1472]," ergibt ",[571,3282,3284,3300],{"className":3283},[574],[571,3285,3287],{"className":3286},[578],[580,3288,3289],{"xmlns":582},[584,3290,3291,3297],{},[587,3292,3293,3295],{},[590,3294,1423],{},[602,3296,2057],{},[624,3298,3299],{"encoding":626},"-4",[571,3301,3303],{"className":3302,"ariaHidden":607},[631],[571,3304,3306,3310,3313],{"className":3305},[635],[571,3307],{"className":3308,"style":3309},[639],"height:0.7278em;vertical-align:-0.0833em;",[571,3311,1423],{"className":3312},[648],[571,3314,2057],{"className":3315},[648]," statt ",[571,3318,3320,3333],{"className":3319},[574],[571,3321,3323],{"className":3322},[578],[580,3324,3325],{"xmlns":582},[584,3326,3327,3331],{},[587,3328,3329],{},[602,3330,2057],{},[624,3332,2057],{"encoding":626},[571,3334,3336],{"className":3335,"ariaHidden":607},[631],[571,3337,3339,3342],{"className":3338},[635],[571,3340],{"className":3341,"style":1722},[639],[571,3343,2057],{"className":3344},[648],".",[3121,3347,3348,3349,3377,3378,3345],{},"Im Nenner die Funktionswerte statt der ",[571,3350,3352,3365],{"className":3351},[574],[571,3353,3355],{"className":3354},[578],[580,3356,3357],{"xmlns":582},[584,3358,3359,3363],{},[587,3360,3361],{},[598,3362,600],{},[624,3364,600],{"encoding":626},[571,3366,3368],{"className":3367,"ariaHidden":607},[631],[571,3369,3371,3374],{"className":3370},[635],[571,3372],{"className":3373,"style":789},[639],[571,3375,600],{"className":3376},[648,652],"-Werte abziehen. Unten steht immer ",[571,3379,3381,3407],{"className":3380},[574],[571,3382,3384],{"className":3383},[578],[580,3385,3386],{"xmlns":582},[584,3387,3388,3404],{},[587,3389,3390,3396,3398],{},[595,3391,3392,3394],{},[598,3393,600],{},[602,3395,619],{},[590,3397,1423],{},[595,3399,3400,3402],{},[598,3401,600],{},[602,3403,604],{},[624,3405,3406],{"encoding":626},"x_1 - x_0",[571,3408,3410,3465],{"className":3409,"ariaHidden":607},[631],[571,3411,3413,3416,3456,3459,3462],{"className":3412},[635],[571,3414],{"className":3415,"style":1320},[639],[571,3417,3419,3422],{"className":3418},[648],[571,3420,600],{"className":3421},[648,652],[571,3423,3425],{"className":3424},[656],[571,3426,3428,3448],{"className":3427},[660,661],[571,3429,3431,3445],{"className":3430},[665],[571,3432,3434],{"className":3433,"style":670},[669],[571,3435,3436,3439],{"style":673},[571,3437],{"className":3438,"style":678},[677],[571,3440,3442],{"className":3441},[682,683,684,685],[571,3443,619],{"className":3444},[648,685],[571,3446,693],{"className":3447},[692],[571,3449,3451],{"className":3450},[665],[571,3452,3454],{"className":3453,"style":700},[669],[571,3455],{},[571,3457],{"className":3458,"style":1364},[710],[571,3460,1423],{"className":3461},[1368],[571,3463],{"className":3464,"style":1364},[710],[571,3466,3468,3471],{"className":3467},[635],[571,3469],{"className":3470,"style":1264},[639],[571,3472,3474,3477],{"className":3473},[648],[571,3475,600],{"className":3476},[648,652],[571,3478,3480],{"className":3479},[656],[571,3481,3483,3503],{"className":3482},[660,661],[571,3484,3486,3500],{"className":3485},[665],[571,3487,3489],{"className":3488,"style":670},[669],[571,3490,3491,3494],{"style":673},[571,3492],{"className":3493,"style":678},[677],[571,3495,3497],{"className":3496},[682,683,684,685],[571,3498,604],{"className":3499},[648,685],[571,3501,693],{"className":3502},[692],[571,3504,3506],{"className":3505},[665],[571,3507,3509],{"className":3508,"style":700},[669],[571,3510],{},[3121,3512,3513],{},"Mittlere und momentane Änderungsrate verwechseln. Der Differenzenquotient sagt nichts über die Steigung an einer einzelnen Stelle.",{"title":3515,"searchDepth":3516,"depth":3516,"links":3517},"",2,[3518,3519,3520],{"id":560,"depth":3516,"text":561},{"id":1828,"depth":3516,"text":1829},{"id":3115,"depth":3516,"text":3116},[3522,3525,3528,3530,3532],{"lhs":3523,"rhs":3524},"(f1 - f0)\u002F(x1 - x0)","(f0 - f1)\u002F(x0 - x1)",{"lhs":3526,"rhs":3527},"((x+h)^2 - x^2)\u002Fh","2*x + h",{"lhs":3529,"rhs":2057},"(3^2 - 1^2)\u002F(3 - 1)",{"lhs":3531,"rhs":2802},"(5*3^2 - 5*1^2)\u002F(3 - 1)",{"lhs":3533,"rhs":2791},"5*3^2","x_0 \\neq x_1,\\ f \\text{ an beiden Stellen definiert}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo 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