Differentialrechnung
From SkyWiki
(Difference between revisions)
| 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>\frac 1{n+1} \cdot x^{n+1}</math> | + | |<math>\frac 1{n+1} \cdot x^{n+1}+C</math> |
|- | |- | ||
|<math>e^x</math> | |<math>e^x</math> | ||
| Line 22: | Line 22: | ||
|<math>a^x</math> | |<math>a^x</math> | ||
|<math>(\ln\,a) \cdot a^x</math> | |<math>(\ln\,a) \cdot a^x</math> | ||
| - | |||
|- | |- | ||
|<math>\ln x</math> | |<math>\ln x</math> | ||
|<math>\frac 1 x</math> | |<math>\frac 1 x</math> | ||
| - | |||
|- | |- | ||
|<math>\log_a x</math> | |<math>\log_a x</math> | ||
|<math>\frac 1 {\ln a \cdot x} = log_a e \cdot \frac 1 x</math> | |<math>\frac 1 {\ln a \cdot x} = log_a e \cdot \frac 1 x</math> | ||
| - | |||
|- | |- | ||
|<math>\sin x</math> | |<math>\sin x</math> | ||
| Line 60: | Line 57: | ||
|<math>\sinh x</math> | |<math>\sinh x</math> | ||
|<math>\cosh x</math> | |<math>\cosh x</math> | ||
| + | |<math>\cosh x+C</math> | ||
| + | |- | ||
| + | |<math>\cosh x</math> | ||
| + | |<math>\sinh x</math> | ||
| + | |<math>\sinh x+C</math> | ||
| + | |- | ||
| + | |<math>\tanh x</math> | ||
| + | |<math>\frac 1 {\cosh^2 x} = 1-\tanh^2 x</math> | ||
| + | |- | ||
| + | |<math>\coth x</math> | ||
| + | |<math>-\frac 1 {sinh^2 x} = 1-coth^2 x</math> | ||
|<math></math> | |<math></math> | ||
| + | |- | ||
| + | |<math>\arsinh x</math> | ||
| + | |<math>\frac 1 \sqrt{x^2+1}</math> | ||
|- | |- | ||
|<math></math> | |<math></math> | ||
| + | |<math></math> | ||
| + | |- | ||
| + | |<math></math> | ||
| + | |<math></math> | ||
| + | |- | ||
| + | |<math></math> | ||
| + | |<math></math> | ||
| + | |- | ||
|<math></math> | |<math></math> | ||
|<math></math> | |<math></math> | ||
Revision as of 07:06, 17 September 2008
| Funktion | Ableitung | Integral |
