If F(x) = f(g(x)), where f(−1) = 6, f '(−1) = 3, f '(3) = 3, g(3) = −1, and g'(3) = 3, find F '(3).

Question

F '' '(3) = ?

please explain and find answer

Answer 1

If F(x) = f(g(x)), then, by the Chain Rule, F'(x) = f'(g(x))g'(x).

So, F'(3) = f'(g(3))g'(3) = f'(-1)(3) = (3)(3) = 9