If F(x) = f(g(x)), where f(1) = 3, f '(1) = 3, f '(5) = 5, g(5) = 1, and g'(5) = 5, find F '(5).

Question

F '(5) = ?

please explain and show answer

Answer 1

F(x) = f(g(x))

By the Chain Rule, F'(x) = f'(g(x))g'(x)

So, F'(5) = f'(g(5))g'(5) = f'(1)g'(5) = (3)(5) = 15