Ableitungen

sabasta
Flashcards by sabasta, updated more than 1 year ago
sabasta
Created by sabasta about 5 years ago
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Description

Gängige Ableitungen aus der Differentialrechnung.

Resource summary

Question Answer
\[f(x)=a^x\] \[ f'(x)=a^x \cdot \ln a \]
\[ f(x)=\sin x \] \[ f'(x)=\cos x \]
\[ f(x)=\cos x \] \[ f'(x)=-\sin x \]
\[ f(x)=C \cdot g(x) \] \[ f'(x)=C \cdot g'(x) \]
\[ f(x)=[g(x)]^n \] \[ f'(x)=n \cdot [g(x)]^{n-1} \cdot g'(x) \]
\[ f(x)=e^x \] \[ f'(x)=e^x \]
\[ f(x)=e^{g(x)} \] \[ f'(x)=e^{g(x)} \cdot g'(x) \]
\[ f(x)=\sin g(x) \] \[ f'(x)=\cos g(x) \cdot g'(x) \]
\[ f(x)=\cos g(x) \] \[ f'(x)=-\sin g(x) \cdot g'(x) \]
\[ f(x)=\tan x \] \[ f'(x)=\frac{1}{cos^2 \cdot x} \]
\[ f(x)=\ln x \] \[ f'(x)=\frac{1}{x} \]
\[ f(x)=\ln g(x) \] \[ f'(x)=\frac{g'(x)}{g(x)} \]
\[ f(x)=log_a g(x) \] \[ f'(x)=\frac{g'(x)}{g(x) \cdot \ln a} \]
\[ f(x)=log_a x \] \[ f'(x)=\frac{1}{x \cdot \ln a} \]
\[ f(x)=a^{g(x)} \] \[ f'(x)=a^{g(x)} \cdot \ln a \cdot g'(x) \]
Kettenregel \[ f(x)= f(g(x)) \] \[ f'(x)=f'(g) \cdot g'(x) \]
Produktregel \[ f(x)=u(x) \cdot v(x) \] \[ f'(x)=u'(x) \cdot v(x) + u(x) \cdot v'(x) \]
Summenregel \[ f(x)=u(x) \pm v(x) \] \[ f'(x)=u'(x) \pm v'(x) \]
Quotientenregel \[ f(x)=\frac{u(x)}{v(x)} \] \[ f'(x)=\frac{u'(x) \cdot v(x) - u(x) \cdot v'(x)}{[v(x)]^2} \]
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