3.1 Basic Differentiation Rules

In this lesson, you will learn about basic differentiation rules including power function, sum, difference, constant multiple, product, and quotient.

Lesson Objectives

Upon completion of the lesson 3.1, you will be able to:

• • Apply the basic differentiation rules to find the derivative of a function.

  • Apply the basic differentiation rules to find the second, third, or higher derivatives.

  • Find the derivative using several basic differentiation rules.

Lesson Content

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

• 1. YouTube video: Derivative of a Linear Function

• 1. YouTube video: Derivative of Power Functions

• 1. YouTube video: Derivative of Polynomial Functions

• 1. YouTube video: The Product Rule

• 1. YouTube video: Product Rule

• 1. YouTube video: Quotient Rule (Power rule, linearity, product rule, reciprocal rule, quotient rule)

• 1. Calculation of Derivative [University of Houston]

  2. YouTube video: Higher Order Derivatives

  3. Please note the correction on the last problem. The acceleration at t = 2 should be -32 ft/sec2.

• 1. Chapter 3 – 3.3: Rules for differentiation (constant multiple rule, sum and difference rules, product rule, quotient rule, higher order derivatives)

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. Differentiation Formulas [Paul's Online Math Notes]

2. Product and quotient rules [Paul's Online Math Notes]

3. Higher order derivatives [Paul's Online Math Notes]

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. Differentiation formulas [Paul's Online Math Notes] (solutions provided) Skip problems #13, 14, 17, 18, 19.

  2. Power Rule [Khan Academy] (and Derivative of Polynomials)

  3. Note: If this link opens in Internet Explorer, then you will be told to upgrade your browser. If that happens, then copy and paste the url that appears into Firefox, Safari or Chrome.

  4. Product and quotient rule [Paul's Online Math Notes] (solutions provided) Skip problems #10 & 11.

  5. Some differentiation formulas with Practice problems [University of Houston]

  6. The d/dx notation, higher order derivatives [University of Houston] (Practice problems with answers and solutions)

Additional Resources

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

• 1. YouTube video: Basic Differentiation Rules

• 1. YouTube video: Tangent Line: Finding the Equation Note: Skip the third example using y=(1+2x)2 (i.e. skip the time period from 5:07 to 6:58).

1. Derivatives: Lesson 17 – Differentiation Rules [Internet Archive]

   1. The module includes information on constant rule, constant multiple rule, power rule, sum rule, difference rule, product rule, quotient rule, and homework.

   2. YouTube video: The Quotient Rule