What is h'(0) equal to

Question

Suppose h = f∘g. Find h'(0) given that f(0) = 5, f '(2) = −5, g(0) = 2, and g'(0) = 8.

h'(0)=

Answer 1

h(x) = f·g = f(g(x))

f(0) = 5

f '(2) = −5

g(0) = 2

g'(0) = 8

Use the chain rule to differentiate:

h'(x) = f'(g(x)) * g'(x)

h'(0) = f'(g(0)) * g'(0) = f'(2) * 8 = -5 * 8 = -40