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Logarithmic Derivation

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z overview
The formula

$\displaystyle f'(x) = f(x) \frac{d}{dx}\ln\vert f(x)\vert $

can be used to determine the derivative of functions $ y = g(x)^{h(x)}$ with $ g(x)>0$ . One obtains

$\displaystyle \frac{d y}{dx}=g(x)^{h(x)}\frac{d}{dx}\big( h(x) \ln g(x) \big) \;. $

(Authors: App/Höllig/Abele )
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  automatically generated 4/ 8/2008