Don't know how to do

Question

If F(x)=f(g(x)), where f(−2)=8, f'(−2)=7, f'(−5)=2, g(−5)=−2 find F'(−5)

Answer 1

F(x) = f(g(x))

So by the Chain Rule, the derivative of F is

F'(x) = f'(g(x))g'(x)

If x is 5, then

F'(-5) = f'(g(-5))g'(-5)

To find the value of this, we'd need to know what g'(-5) is.

(Are you sure you copied the problem correctly? There should be a g'(-5) in there.) Then

F'(-5) = f'(g(-5))g'(-5) = f'(-2)g'(-5) = 7g'(-5)