Differentialrechnung

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{|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>
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|<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 MathImage Ableitung MathImage Integral MathImage
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