AN 2.1 Ableitungsregeln

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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