3.3 The Chain Rule

In this lesson, you will learn about the power chain rule and the derivative of a composition of two, three or more functions.

Lesson Objectives

Upon completion of the lesson 3.3, you will be able to:

• • Apply the Power Chain Rule.

  • Apply the Chain Rule to find the derivative of a composition of two functions.

  • Apply the Chain Rule to find the derivative of a composition of three or more functions.

Lesson Content

View all of the following instructional videos. These will help you master the objectives for this module.

• 1. YouTube videos: Chain Rule

  2. Part 3.07a:

• 1. Part 3.07b:

• 1. YouTube videos: Chain Rule Example

  2. Part 3.07c:

• 1. Part 3.07d:

Lesson Readings

The following required readings cover the content for this module. As you go through each reading, pay close attention to the content that will help you learn the objectives for this module.

1. Derivatives: Lesson 18- The Chain Rule [Internet Archives]

   1. The module includes information on chain rule definition, the chain rule with other rules, and homework. View only the sections on the chain rule definition and the chain rule with other rules, and do the homework problems.

   2. The Chain Rule [Dartmouth] (statement of the Chain Rule, applying the Chain Rule)

   3. Chain Rule [Paul's Online Math Notes]

   4. Skip examples 2c, 2d, 3b, 3c, 4a, and 5a. Read only up to and including Example 5b.

Lesson Practice Exercises/Activities

Make your way through each of the practice exercises. This is where you will take what you have learned from the lesson content and lesson readings and apply it by solving practice problems.

• 1. Drill - Chain Rule [University of Tennessee]

  2. Note: Do not do the 2nd, 6th, and 10th problem.

  3. Chain Rule [Paul's Online Math Notes]

  4. Note: Do only problems #1 - 6, 13, 15, 17, 19, 20, 23, 26, 27.

  5. Drill-Chain Rule [Visual Calculus]

  6. Note: Skip the 2nd, 6th, and 10th problem.

Additional Resources

Below are additional resources that help reinforce the content for this module.

1. Lecture 15: The Chain Rule [Prairie State College] (identifying compositions of functions and writing a function as a composition of two functions, using the chain rule to differentiate compositions of functions)

2. Leibniz Notation and the Chain Rule University of Houston] (compositions of two functions, three functions, the chain rule in Leibniz Notation) Skip pages 1 & 2. If the link does not take you directly to the site, then please copy and paste the url into your browser.

3. Chain Rule Help [WyzAnt]

4. A Chain Rule Problem [calculus-help.com]