So f of x is just this area right over here. That's all we know about it. We don't know it has anything to do with antiderivatives just yet. That's what we're going to try to prove in this video. So just for fun, let's take the derivative of f. And we're going to do it just using the definition of derivatives and see what we get when we take the derivative using the definition of derivatives. So we would get the derivative f prime of x. Well, this definition of derivatives, it's a limit as delta x approaches 0 of capital F of x plus delta x minus f of x, all of that over delta x.