Now, how can we get a better and better approximation for the slope of the tangent line here? Well, we could take the limit as x approaches a. As x gets closer and closer and closer to a, the secant line slope is going to better and better and better approximate the slope of the tangent line, this tangent line that I have in red here. So we would want to take the limit as x approaches a here. Either way, we're doing a very similar, we're doing the exact same thing. We're finding, we're taking, we have an expression for the slope of a secant line, and then we're bringing those x values of those points closer and closer together, closer and closer together, so the slopes of those secant lines better and better and better approximate that slope of the tangent line, and at the limit, it does become the slope of the tangent line. That is the derivative of, or that's the definition of the derivative.