And I'm going to come up with an expression using both the formal definition and the alternate definition, and that will allow us to compare them a little bit. So let's think about first the formal definition. So the formal definition wants us to find an expression for the derivative of our function at any x. So let's say that this is some arbitrary x right over here. This would be the point x, f of x. And let's say that this is, let's call this x plus h. So this distance right over here is going to be h. This right over here is going to be the point x plus h, f of x plus h. Now the whole underlying idea of the formal definition of limits is to find the slope of the secant line between these two points, and then take the limit as h approaches 0. 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.