August 30 - The derivative

So while today should be fairly momentous as we begin talking about the derivative, it is in fact a review of concepts previously seen at the end of last semester in pre-calculus.

The most important concern is that students remember that the derivative is defined as the limit of the slope between two points. That's it. It's the limit of the difference quotient as the delta x approaches zero.

We began today to study the methods for finding the derivative of a given function. I will continually refer to these methods as "shortcuts" since they do not involve limits at all. I want you to do your best though to always keep in mind the fact that limits are in play however.

The definitions of the derivative, the initial shortcut rules and a couple of examples are included in my notes below.