Mathematics-Online lexicon: Derivative Formula: The Chain Rule

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	Mathematics-Online lexicon:
	Derivative Formula: The Chain Rule

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The derivative of a composition of functions

$\displaystyle h(x)=\left( f \circ g\right)(x)=f\bigl( g(x)\bigr)$

with

$\displaystyle f(y)=z,\quad g(x)=y,\quad h(x)=z$

$\displaystyle h'(x)=f'(g(x))g'(x) \:$ . $\displaystyle$

One also writes

$\displaystyle \frac{dz}{dx}=\frac{dz}{dy}\;\frac{dy}{dx} \:$ . $\displaystyle$

Annotation:

automatically generated 4/ 8/2008