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Derivative Formula: The Chain 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
Example 1:
$\displaystyle f(x)$ $\displaystyle =$ $\displaystyle (x^2+5)^3$  
$\displaystyle f'(x)$ $\displaystyle =$ $\displaystyle 3\cdot(x^2+5)^2\cdot2x$  
  $\displaystyle =$ $\displaystyle 6x(x^2+5)^2$  

Example 2:

$\displaystyle f(x)$ $\displaystyle =$ $\displaystyle e^{x^3+2x}$  
$\displaystyle f'(x)$ $\displaystyle =$ $\displaystyle e^{x^3+2x}\cdot(3x^2+2)$  

Example 3:

$\displaystyle f(x)$ $\displaystyle =$ $\displaystyle \ln(x^2+2x)$  
$\displaystyle f'(x)$ $\displaystyle =$ $\displaystyle \frac{2x+2}{x^2+2x}$  

(Author: unknown)

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  automatisch erstellt am 8.  7. 2004