Differentialrechnung
From SkyWiki
(Difference between revisions)
| Line 1: | Line 1: | ||
{|border=1 | {|border=1 | ||
| - | |'''Funktion''' | + | |'''Funktion <math>f(x)</math>''' |
| - | |'''Ableitung''' | + | |'''Ableitung <math>f'(x)=\frac{d f(x)}{d x}</math>''' |
| + | |'''Integral <math>F(x)=\int f(x)</math>''' | ||
|- | |- | ||
|<math>\sin x</math> | |<math>\sin x</math> | ||
|<math>\cos x</math> | |<math>\cos x</math> | ||
| + | |<math>\-cos x+C</math> | ||
|- | |- | ||
|<math>\cos x</math> | |<math>\cos x</math> | ||
|<math>-\sin x</math> | |<math>-\sin x</math> | ||
| + | |<math>\sin x+C</math> | ||
|- | |- | ||
|<math>\tan x</math> | |<math>\tan x</math> | ||
|<math>\frac 1 {\cos^2 x} = 1+\tan^2 x</math> | |<math>\frac 1 {\cos^2 x} = 1+\tan^2 x</math> | ||
| + | |<math></math> | ||
|- | |- | ||
|<math>\cot x</math> | |<math>\cot x</math> | ||
|<math>-\frac 1 {\sin^2 x} = -(1+\cot^2 x)</math> | |<math>-\frac 1 {\sin^2 x} = -(1+\cot^2 x)</math> | ||
| + | |<math></math> | ||
|- | |- | ||
|<math>\arcsin x</math> | |<math>\arcsin x</math> | ||
|<math>\frac 1 {1-x^2}</math> | |<math>\frac 1 {1-x^2}</math> | ||
| + | |<math></math> | ||
|- | |- | ||
|<math>\arccos x</math> | |<math>\arccos x</math> | ||
|<math>-\frac 1 {1-x^2}</math> | |<math>-\frac 1 {1-x^2}</math> | ||
| + | |<math></math> | ||
|- | |- | ||
|<math>\arctan x</math> | |<math>\arctan x</math> | ||
|<math>\frac 1 {1+x^2}</math> | |<math>\frac 1 {1+x^2}</math> | ||
| + | |<math></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></math> | ||
|- | |- | ||
| + | |<math>e^x</math> | ||
|<math>e^x</math> | |<math>e^x</math> | ||
|<math>e^x</math> | |<math>e^x</math> | ||
| Line 32: | Line 42: | ||
|<math>a^x</math> | |<math>a^x</math> | ||
|<math>(\ln\,a) \cdot a^x</math> | |<math>(\ln\,a) \cdot a^x</math> | ||
| + | |<math></math> | ||
| + | |- | ||
| + | |<math></math> | ||
| + | |<math></math> | ||
| + | |<math></math> | ||
| + | |- | ||
| + | |<math></math> | ||
| + | |<math></math> | ||
| + | |<math></math> | ||
|- | |- | ||
| - | | | + | |<math></math> |
| - | | | + | |<math></math> |
| + | |<math></math> | ||
|- | |- | ||
| - | | | + | |<math></math> |
| - | | | + | |<math></math> |
| + | |<math></math> | ||
|- | |- | ||
| - | | | + | |<math></math> |
| - | | | + | |<math></math> |
| + | |<math></math> | ||
|} | |} | ||
[[category:Mathematik]] | [[category:Mathematik]] | ||
Revision as of 06:33, 17 September 2008
| Funktion | Ableitung | Integral |
