After completing this section, students should be able to do the following.

- Understand the derivative as a function related to the original definition of a function.
- Find the derivative function using the limit definition.
- Relate the derivative function to the derivative at a point.
- Explain the relationship between differentiability and continuity.
- Relate the graph of the function to the graph of its derivative.
- Determine whether a piecewise function is differentiable.