Math 22 Chain Rule

The Chain Rule

 If $y=f(x)$ is a differentiable function of $u$ and $u=g(x)$ is a 
 differentiable function of $x$, then $y=f(g(x))$ is a differentiable function 
 of $x$ and
 
 ${\frac {dy}{dx}}={\frac {dy}{du}}\cdot {\frac {du}{dx}}$
 
 In another word, ${\frac {d}{dx}}[f(g(x))]=f'(g(x))\cdot g'(x)$

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