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Mathematics-Online course: Preparatory Course Mathematics - Analysis - Differential Calculus

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

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

is

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

One also writes

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

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  automatically generated 1/9/2017