Derivative outer function and left inner functions untouched, then derivative inner, left another inner functions untouched, then derivative inner-inner function, and so on.
f(x) = sin x, g(x) = tan x, h(x) = sin x i(x) = √x, \(f(g(h(i(x)))) = sin(tan(sinx^{\frac{1}{2}})\)
\[\frac{d}{dx} f(g(h(i(x)))) = f'(g(h(i(x)))) \cdot g'(h(i(x))) \cdot h'(i(x)) \cdot i'(x)\]