Mathematics-Online lexicon: Derivative Formula: The Power Rule

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	Mathematics-Online lexicon:
	Derivative Formula: The Power Rule

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

Power rule:

$\displaystyle f(x)$	$\displaystyle =$	$\displaystyle ax^n$
$\displaystyle f'(x)$	$\displaystyle =$	$\displaystyle nax^{n-1}\qquad \textnormal{for all } x \in \mathbf{D}\textnormal{, }a=\textnormal{const} \textnormal{, }n \not=0$

notice:

$\displaystyle f(x)$	$\displaystyle =$	$\displaystyle a\qquad\textnormal{for all }a=\textnormal{const}$
$\displaystyle f'(x)$	$\displaystyle =$	0

(Authors: Jahn/Knödler)

Example:

automatically generated 7/ 8/2004