composition derivative rule

Let g(x) and f(x) be real-valued functions, and let g(x) be differentiable at x_0 and f(x) differentiable at g(x_0). Then the function h(x) = f(g(x)) is differentiable at x_0 with h'(x_0) = f'(g(x_0)) g'(x_0).

derivative | differentiable function

Gottfried Leibniz