Category:Derivative of Composite Function

This category contains pages concerning Derivative of Composite Function:

Let $f, g, h$ be continuous real functions such that:

$\forall x \in \R: \map h x = \map {f \circ g} x = \map f {\map g x}$

Then:

$\map {h'} x = \map {f'} {\map g x} \map {g'} x$

where $h'$ denotes the derivative of $h$.

Using the $D_x$ notation:

$\map {D_x} {\map f {\map g x} } = \map {D_{\map g x} } {\map f {\map g x} } \map {D_x} {\map g x}$

This is often informally referred to as the chain rule (for differentiation).