As h gets closer and closer, this blue point is going to get closer and closer and closer to x, and this point is going to approach it on the curve, and the secant line is going to become a better and better and better approximation of the tangent line at x. So let's actually do that. So what's the slope of the secant line? Well, it's the change in your vertical axis, which is going to be f of x plus h minus f of x over the change in your horizontal axis. And that's x plus h minus x, and we see here the difference is just h over h. And we're going to take the limit of that as h approaches 0. So in the case when f of x is the natural log of x, this will reduce to the limit as h approaches 0, f of x plus h is the natural log of x plus h minus the natural log of x, all of that over h. So this right over here, for our particular f of x, this is equal to f prime of x. So if we wanted to evaluate this, when x is equal to e, then everywhere we see an x, we just have to replace it with an e. This is essentially expressing our derivative as a function of x.