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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 overview

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:


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  automatically generated 7/ 8/2004