Math 205 JW Lecture 9 - The Derivative

Welcome to lecture 9 of Math 205 JW - Elements of Calculus.

In tonight's lecture we start by going over a quiz that was given prior to class, and then go into our main topic of discussion for the class, the all-important Derivative! (Capitalized for emphasis.)

We develop the derivative by searching for a way to measure instantaneous rate of change--how fast something is changing at an instant, as opposed to on average over some interval. We use three main ideas to develop this--the interpretation of slope as a rate, the average rate of change formula, and limits.

We derive the formula for the derivative using limits (a VERY important formula--the limit of the difference quotient as the denominator approaches zero), talk about its notation and do tons of examples, explaining what the answers mean. We also show how to find the equation of a tangent line, which is something that is important to know how to do in a calculus class.

We also talk about some interpretations of derivatives--slope, slope of the tangent line, rate of change, formula for the slope at a point, how fast something is moving at an instant, etc.

We will talk more about derivatives, their interpretations and applications in the next class.