Differentialrechnung

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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></math>
 
|-
|-
|<math>\ln x</math>
|<math>\ln x</math>
|<math>\frac 1 x</math>
|<math>\frac 1 x</math>
-
|<math></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></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

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