## Calculus: Early Transcendentals 8th Edition

$$F'(5)=24$$
$$F(x)=f(g(x))$$ Apply the Chain Rule, we have $$F'(x)=\frac{d[f(g(x))]}{d[g(x)]}\frac{d[g(x)]}{dx}$$ $$F'(x)=f'(g(x))\times g'(x)$$ Therefore, $$F'(5)=f'(g(5))\times g'(5)$$ We have $g(5)=-2$ and $g'(5)=6$. So, $$F'(5)=f'(-2)\times6$$ We also have $f'(-2)=4$. Therefore, $$F'(5)=4\times6=24$$