Suppose h = f∘g. Find h'(0) given that f(0) = 7, f '(2) = −9, g(0) = 2, and g'(0) = 9.

Answer 1

This is the chain rule: f(g(x))' = f'(g(x))*g'(x).

Thus, h'(0) = f'(g(0))g'(0) = f'(2)*9 = -9 * 9 = - 81