composite function

The derivative of a composite function is given by the formula: \[
D[f(g(x))] = f'(g(x)) \cdot g'(x)\]

Given two functions \( f(x) \) and \( g(x) \), the composite function \( g \circ f \) is defined as the function obtained by first applying \( f \) to the input \( x \), and then applying \( g \) to the result \( f(x) \). Formally:
\[
g \circ f = g(f(x))
\]