As your change of x gets smaller and smaller and smaller, you're going to get a better and better approximation. Your change of y is going to get smaller and smaller and smaller. So what you want to do, and we're going to go into depth into all of this and study it more rigorously, is you want to take the limit as delta x approaches 0 of your change in y over your change in x. And when you do that, you're going to approach that instantaneous rate of change. You could view it as the instantaneous slope at that point in the curve, or the slope of the tangent line at that point in the curve. Or if we use calculus terminology, we would view that as the derivative. So the instantaneous slope is the derivative.