5.6.1 Why hand calculation?

Since our introduction of the derivative in Chapter 2, we have gradually expanded our repertoire of formulas for calculating derivatives of functions defined by formulas. Along the way, we have frequently asked you, in Checkpoints and Exercises, to calculate derivatives. Such calculation is not the main point of this course — indeed, relatively inexpensive electronic devices can calculate the derivative of any formula-defined function quickly, easily, and accurately. However, it is still important that you develop an appropriate level of competence in pencil-and-paper calculation of derivatives. There are several reasons for this:

• You need to know when it is quicker and easier to do your own calculation than to use an electronic device — or to interpret its output. Accurate and confident judgment about proper use of tools comes only from lots of practice.

• You need to be able to recognize wrong results from your computer or calculator — usually the result of wrong entry of the problem. Practice with hand calculation will help you develop a sense of the types of components that can turn up in a given derivative calculation.

• In the next chapters we will confront the much harder — and more important — problem of finding antiderivatives. We will see that skill in derivative calculation is an essential part of this process.

In this section we review the important formulas that have appeared in our development thus far, and we illustrate how several different formulas may be needed in a single calculation.