Section Summary

In this section, we developed two new differentiation formulas, one specific and the other general. The specific formula is for the square root function. You may have noticed that this is consistent with the Power Rule, previously known to us only for nonnegative integer powers and the `-1` power:

The new general formula is the most important of the differentiation rules, the Chain Rule:

We have put our new differentiation formulas to work to see that a physical optimization law — Fermat's Principle — implies equality of angles of incidence and reflection. This is not a terribly profound conclusion, and it could be deduced without any calculus at all (see Exercise 19). However, we have also laid the groundwork for addressing more difficult questions, such as the refraction question we posed at the start of the chapter. That issue will be taken up in a project associated with this chapter.