CALCULUS QUESTIONS

Question

Given F(x)=f(g(x)), where f(3)=4, f'(-4)=8, f(3)=5, g(3)=-4 and g'(3)=6. Find F'(3)

Answer 1

The chain rule states that F'(x) = f'(g(x))g'(x)

Thus, to find F'(3), we need g'(3) and f'(g(3))

g'(3) = 6

As g(3) = -4, f'(g(3)) = f'(-4) = 8

Then, f'(g(3))g'(3) = f'(4)g'(3) = 8 * 6 = 48