Differentialrechnung

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Line 1: Line 1:
{|border=1
{|border=1
|'''Funktion <math>f(x)</math>'''
|'''Funktion <math>f(x)</math>'''
-
|'''Ableitung <math>f'(x)=\frac{d f(x)}{d x}d x</math>'''
+
|'''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></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>
Line 58: Line 54:
|<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 MathImage Ableitung MathImage Integral MathImage
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