If F(x) = f(g(x)), where f(4) = 5, f '(4) = 6, f '(3) = 4, g(3) = 4, and g'(3) = 2, find F '(3).

Answer 1

H(x) = f(g(x))

H'(x) = f'(g(x)) g'(x) by chain rule

H'(3) = f'(g(3))g'(3) = f'(4)g'(3) = 6*2 = 12