Let h(x) = f(g(x)) where g(1) = 2,f′(2) = 5 and g′(1) = 6. Find h′(1).

Answer 1

h(x) = f(g(x))

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

So, h'(1) = f'(g(1))g'(1) = f'(2)(6) = (5)(6) = 30