Unit 6 – Sections 3.6, 3.7, 3.10
Module Overview
This is a highly focused unit – nothing but the Chain Rule and some of its applications. We delve much more deeply into applications of our material to other courses in the examples (with even more examples to come in the following units). If you are comfortable with the Chain Rule, but apply it without using the Leibniz notation, make sure to watch the videos. There are a number of applications where the d/dx notation becomes necessary.
Learning Outcomes
- While the Power Rule, Sum Rule, and other basic facts of derivatives become second nature, the Chain Rule starts to seem to be the most powerful of the lot. As we advance in the course, we will find more and more places that require the Chain Rule. In this unit we introduce the rule and show how to apply it using the Leibniz (d/dx) notation.
- Implicit Differentiation is generally taught in high schools as the beginning of the really difficult derivatives. In this unit we see that it is simply our first application of the Chain Rule. Once the idea is accepted, the entire section is reduced to this one concept.
- In this unit, we find that Related Rates problems are simply word problems that require the Chain Rule – nothing more.
Related Project Resources
