\section*{Introduction}

In this module, you will meet the notion of the {\bf derivative}.
The observations that we made in Module 1 regarding average rates of
change approximating the exact rate of change will be formalized,
and we will see how the numbers we were trying to approximate can be
determined explicitly and directly.  Moreover, we will begin to see
how the rate of change can be a powerful tool in understanding
functions.

This is the first of the two theory modules.  In these modules, we
will excuse ourselves from the applications in order to develop
technical skills.  In particular, after completing this module, you
will be able to determine the derivative function of most functions
defined using algebraic formulas and other elementary functions.

This module has two primary goals.  The first is to understand the
meaning of the derivative function and use it to make precise
observations about the behavior of functions.  The second is to be
able to be able to differentiate functions when given their
algebraic definitions.
