4.2 Implicit Differentiation

In this lesson, you will learn about using implicit differentiation to find the first and second derivatives.

Lesson Objectives

Upon completion of the lesson 4.2, you will be able to:

• • Find the first derivative using implicit differentiation.

  • Find the second derivative using implicit differentiation.

Lesson Content

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

• 1. YouTube videos: Implicit Differentiation

  2. Part 3.10a:

• 1. Part 3.10b:

• 2. Part 3.10c:

• 1. Part 3.10d:

• 1. YouTube video: Implicit Differentiation - More Examples

• 1. Implicit Differentiation - Extra Examples

• 2. Finding a Second Derivative Using Implicit Differentiation

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 23 - Implicit differentiation [Internet Archive]

  2. The module includes information on (first) derivatives of implicitly defined functions and homework with answers.

  3. Implicit Differentiation [Paul's Online Math Notes]

  4. Note: Skip example 2c, 5c, and 6.

1. Implicit Differentiation [UMass Lowell]

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. Implicit Differentiation [City Colleges of Chicago] (sample problems with answers, practice problems with answers)

  2. Note: Skip #5e, 5k, 5m from the Practice Problems.

  3. Implicit Differentiation [Paul's Online Math Notes] (with solutions) Do only problems #1 - 5, 7, 9, 10.

  4. Implicit Differentiation problems [UC Davis] (with solutions) Skip problem #5.

  5. Higher Order Derivatives using Implicit Differentiation [Paul's Online Math Notes] (with solutions) Do only problems #10 & 11.

Additional Resources

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

• 1. YouTube video: Trig Implicit Differentiation Example

• 1. YouTube video: Implicit Differentiation (part 2)