The Formula you linked actually has a little bit more to it in order to understand it intuitively. You know it better as (Y2-Y1)/(X2-X1). It's literally the slope formula. However, instead of Y1, we use "f(x)". Instead of Y2, we use "f(x+h)" where h represents how far away x-wise the second point is from the first. For X1 we just use X, and for X2 we use "x+h". The thing is, the top stays exactly like you'd expect. The bottom however simplifies pretty significantly, because when you subtract x from (x+h), you just get h. Calculus, at least Derivatives, revolve around what happens when h gets very very small, or when the two points you're finding the slope between get very close together. The closer they get, the less the slope changes, and by looking at those patterns we can see what the slope is heading towards if those two points were to intersect. This is terrible terrible official form and people will go all ape**** to hear me say it, but in layman's terms, Derivatives represent the instantaneous slope of a curve at a given point. - your friendly, lowly, high school math teacher.