Derivative of Composite Function (Chain Rule)

If u = f(x) and y = F(u), then y = F(f(x)) is the composition of f and F. u is called the intermediate argument.

If u = f(x) has the derivative f′(x) and y = F(u) has the derivative F′(u), then the function of a function F(f(x)) has the derivative equal to F′(u) f′(x), where in place of u you must substitute u = f(x).