F(x)=g(h(x)), g(2)=3, g’(2)=3, h(0)=2, h’(0)=5, Find F’(0)

Answer 1

F(x) = g(h(x))

Using the Chain Rule, F'(x) = g'(h(x))h'(x).

So, F'(0) = g'(h(0))h'(0) = g'(2)h'(0) = (3)(5) = 15

Answer 2

apply the chain rule

F'(x) = (g(h))' = g'(h)h'

substitute in values now.