Flashcards
AN 2.1 Ableitungsregeln
Cards in this deck (19)
- 1\[f(x)=a^x\]\[ f'(x)=a^x \cdot \ln a \]
- 2\[ f(x)=\sin x \]\[ f'(x)=\cos x \]
- 3\[ f(x)=\cos x \]\[ f'(x)=-\sin x \]
- 4\[ f(x)=C \cdot g(x) \]\[ f'(x)=C \cdot g'(x) \]
- 5\[ f(x)=[g(x)]^n \]\[ f'(x)=n \cdot [g(x)]^{n-1} \cdot g'(x) \]
- 6\[ f(x)=e^x \]\[ f'(x)=e^x \]
- 7\[ f(x)=e^{g(x)} \]\[ f'(x)=e^{g(x)} \cdot g'(x) \]
- 8\[ f(x)=\sin g(x) \]\[ f'(x)=\cos g(x) \cdot g'(x) \]
- 9\[ f(x)=\cos g(x) \]\[ f'(x)=-\sin g(x) \cdot g'(x) \]
- 10\[ f(x)=\tan x \]\[ f'(x)=\frac{1}{cos^2 \cdot x} \]
- 11\[ f(x)=\ln x \]\[ f'(x)=\frac{1}{x} \]
- 12\[ f(x)=\ln g(x) \]\[ f'(x)=\frac{g'(x)}{g(x)} \]
- 13\[ f(x)=log_a g(x) \]\[ f'(x)=\frac{g'(x)}{g(x) \cdot \ln a} \]
- 14\[ f(x)=log_a x \]\[ f'(x)=\frac{1}{x \cdot \ln a} \]
- 15\[ f(x)=a^{g(x)} \]\[ f'(x)=a^{g(x)} \cdot \ln a \cdot g'(x) \]
- 16Kettenregel \[ f(x)= f(g(x)) \]\[ f'(x)=f'(g) \cdot g'(x) \]
- 17Produktregel \[ f(x)=u(x) \cdot v(x) \]\[ f'(x)=u'(x) \cdot v(x) + u(x) \cdot v'(x) \]
- 18Summenregel \[ f(x)=u(x) \pm v(x) \]\[ f'(x)=u'(x) \pm v'(x) \]
- 19Quotientenregel \[ f(x)=\frac{u(x)}{v(x)} \]\[ f'(x)=\frac{u'(x) \cdot v(x) - u(x) \cdot v'(x)}{[v(x)]^2} \]
Information
- Description
- Gängige Ableitungen aus der Differentialrechnung.
- Created by
- Deleted user · Feb 2017
- Updated
- Feb 14, 2017
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- Created by sabasta · Feb 13, 2016
- Copied by Mathe Queen · Feb 7, 2017
- Copied by Mathe Queen · Feb 14, 2017
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