Question

If F(x) = f(g(x)), where f(-2) = 5, f'(-2) = 9, f'(4) = 3, g(4) = -2, and g'(4) = 4, find F'(4).

F'(4) =

Answer 1

36.

Explanation:

o find F'(4), we need to use the chain rule of differentiation. The chain rule states that if F(x) = f(g(x)), then F'(x) = f'(g(x)) * g'(x).

Given that f(-2) = 5, f'(-2) = 9, f'(4) = 3, g(4) = -2, and g'(4) = 4, we can calculate F'(4) as follows:

F'(4) = f'(g(4)) * g'(4) = f'(-2) * g'(4) = 9 * 4 = 36

Therefore, F'(4) = 36.