Differentialrechnung
From SkyWiki
(Difference between revisions)
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{|border=1 | {|border=1 | ||
|'''Funktion <math>f(x)</math>''' | |'''Funktion <math>f(x)</math>''' | ||
| - | |'''Ableitung <math>f'(x)=\frac{d f(x)}{d x} | + | |'''Ableitung <math>f'(x)=\frac{d f(x)}{d x}</math>''' |
| - | |'''Integral <math>F(x)=\int f(x)</math>''' | + | |'''Integral <math>F(x)=\int f(x) d x</math>''' |
|- | |- | ||
|<math>b</math> | |<math>b</math> | ||
| Line 14: | Line 14: | ||
|<math>x^n</math> | |<math>x^n</math> | ||
|<math>n \cdot x^{n-1}</math> | |<math>n \cdot x^{n-1}</math> | ||
| - | |<math></math> | + | |<math>\frac 1{n+1} \cdot x^{n+1}</math> |
|- | |- | ||
|<math>\sin x</math> | |<math>\sin x</math> | ||
| Line 32: | Line 32: | ||
|<math>\arcsin x</math> | |<math>\arcsin x</math> | ||
|<math>\frac 1 {1-x^2}</math> | |<math>\frac 1 {1-x^2}</math> | ||
| - | |||
|- | |- | ||
|<math>\arccos x</math> | |<math>\arccos x</math> | ||
|<math>-\frac 1 {1-x^2}</math> | |<math>-\frac 1 {1-x^2}</math> | ||
| - | |||
|- | |- | ||
|<math>\arctan x</math> | |<math>\arctan x</math> | ||
|<math>\frac 1 {1+x^2}</math> | |<math>\frac 1 {1+x^2}</math> | ||
| - | |||
|- | |- | ||
|<math>\operatorname{arccot} x</math> | |<math>\operatorname{arccot} x</math> | ||
|<math>-\frac 1 {1+x^2}</math> | |<math>-\frac 1 {1+x^2}</math> | ||
| - | |||
|- | |- | ||
|<math>e^x</math> | |<math>e^x</math> | ||
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|<math></math> | |<math></math> | ||
|- | |- | ||
| - | |<math></math> | + | |<math>\log_a x</math> |
| - | |<math></math> | + | |<math>\frac 1 {\ln a \cdot x} = \frac 1 x \cdot log_a e</math> |
|<math></math> | |<math></math> | ||
|- | |- | ||
Revision as of 06:53, 17 September 2008
| Funktion | Ableitung | Integral |
