1. We are given the function composition $F(x) = f(g(x))$. The problem asks for the derivative $F'(-3)$. 2. By the chain rule, the derivative of $F$ at $x$ is $$F'(x) = f'(g(x)) \cdot g'(x).$$ 3. To find $F'(-3)$, substitute $x = -3$: $$F'(-3) = f'(g(-3)) \cdot g'(-3).$$ 4. From the problem, we know: - $g(-3) = -2$ - $g'(-3) = 5$ - $f'(-2) = 6$ 5. Substitute these values: $$F'(-3) = f'(-2) \cdot 5 = 6 \cdot 5 = 30.$$