Limit Definition of Derivative

Oh man, does this formula scare everyone who's ever seen it! On the other hand, you'll never see it again (other than the AP test) because there's quicker ways to take derivatives, so rest easy in the knowledge that a week from now you'll have forgotten all about it. As I describe in the videos below, as long as the delta-x cancels in each problem, you know you got the right answer.

Limit Definition of Derivatives (a.k.a. Difference Quotient)

This video explains that crazy limit equation which contains all those Δx symbols, but first we learn the point of all this derivative nonsense: finding the slope of a function at each point along the curve. Sound crazy? It's the basis of calculus. These problems also show up in pre-calc as the "Difference Quotient": the math is the same, you just might have an "h" instead of Δx.

Hard Limit Definition of Derivatives Problems

In this video I work some more of the same Δx problems, except with way more algebra. If you're in a lighter calc class (or pre-calc doing difference quotients), you may not see anything this hard, but if you're in AP or on your way to a science or engineering degree, buckle up, because this is just a taste of what's to come throughout calculus!