All we did so far is we used something we knew about inverse functions, and we used the chain rule to take the derivative of the left-hand side, but if you divide both sides by g prime of f of x, what are you going to get? You're going to get a relationship between the derivative of a function and the derivative of its inverse. So you get f prime of x is going to be equal to one over all of this business, one over g prime of f of x, g prime of f of x. And this is really neat, because if you know something about the derivative of a function, you can then start to figure out things about the derivative of its inverse. And we can actually see this is true with some classic functions. So let's say that f of x is equal to e to the x, and so g of x would be equal to the inverse of f, so f inverse, which is, what's the inverse of e to the x? Well, one way to think about it is if you have y is equal to e to the x, if you want the inverse, you can swap the variables and then solve for y again.