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.

Type: Video Links
Title	Author	Description
Chain Rule - Introduction \| Chain Rule - Introduction	Shai Cohen
Chain Rule - Statement and Proof \| Chain Rule - Statement and Proof	Shai Cohen
Chain Rule - How to Use \| Chain Rule - How to Use	Shai Cohen
Chain Rule - Ugly Example \| Chain Rule - Ugly Example	Shai Cohen
Chain Rule - Really Ugly Example \| Chain Rule - Really Ugly Example	Shai Cohen
Chain Rule Example - Proof of the Quotient Rule \| Chain Rule Example - Proof of the Quotient Rule	Shai Cohen
Chain Rule Example - Why We Should Use It \| Chain Rule Example - Why We Should Use It	Shai Cohen
Chain Rule Example - Easy \| Chain Rule Example - Easy	Shai Cohen
Chain Rule Example - Ridiculous \| Chain Rule Example - Ridiculous	Shai Cohen
Implicit Differentiation - Introduction \| Implicit Differentiation - Introduction	Shai Cohen
Implicit Differentiation - A Tougher Use \| Implicit Differentiation - A Tougher Use	Shai Cohen
Implicit Differentiation - Same Result, Different Look \| Implicit Differentiation - Same Result, Different Look	Shai Cohen
Implicit Differentiation Example - Flower \| Implicit Differentiation Example - Flower	Shai Cohen
Implicit Differentiation Example - Second Derivative, part 1 \| Implicit Differentiation Example - Second Derivative, part 1	Shai Cohen
Implicit Differentiation Example - Second Derivative, part 2 \| Implicit Differentiation Example - Second Derivative, part 2	Shai Cohen
Implicit Differentiation Example - Tangents \| Implicit Differentiation Example - Tangents	Shai Cohen
Related Rates \| Related Rates	Shai Cohen
Related Rates Example - First Example \| Related Rates Example - First Example	Shai Cohen
Related Rates Example - Shadows, part 1 \| Related Rates Example - Shadows, part 1	Shai Cohen
Related Rates Example - Shadows, part 2 \| Related Rates Example - Shadows, part 2	Shai Cohen