Mathematics

The key is to apply the Fundamental Theorem of Calculus twice. First, differentiating $F(x)$ gives you $F'(x) = f(x)$ directly—that's the theorem in action. Then differentiate again: since $f$ is differentiable, $F''(x)$ is just the derivative of $f(x)$. The answer is simpler than you might expect once you recognize that integration and differentiation are inverse operations.

The key is to apply the Fundamental Theorem of Calculus twice. First, differentiating $F(x)$ gives you $F'(x) = f(x)$ directly—that's the theorem in action. Then differentiate again: since $f$ is differentiable, $F''(x)$ is just the derivative of $f(x)$. The answer is simpler than you might expect once you recognize that integration and differentiation are inverse operations.