Chapter 2.3 - The Product and Quotient Rules and Higher-Order Derivatives

Objectives:

• • Find the derivative of a function using the Product Rule.

  • Find the derivative of a function using the Quotient Rule.

  • Find the derivative of a trigonometric function.

  • Find a higher-order derivative of a function.

Product Rule (for Day #5 lesson)

Introduction to how to differentiate the product of two functions. Learn that sometimes it's optional (and maybe even preferable to use techniques other than the product rule) while other times you'll have no choice but to use the product rule.

Quotient Rule (for Day #7 lesson)

Introduction to how to differentiate the quotient of two functions. Similar to the product rule, sometimes you have options other than quotient rule, but other times you have little choice. (Click image to view example.)

The presence of a radical in the function you are to differentiate will require some careful algebra. I neglected to include such an exercise in the video, but you may click on the above image to see a scan of an annotated example.

Quotient Rule & Tangent Line (for Day #8 lesson)

Finding the tangent line equation for a function at a given point. The differentiation process involves use of the quotient rule.

Higher-Order Derivatives (for Day #8 lesson)

Notation and process for finding second, third, fourth, etc. derivatives of a function.

Practice for the Multiple Choice Assessment on Chapters 1.1-2.3

This assessment will include 10 multiple choice (50% of score) and 10 free response (50% of score) questions.

Since this assessment only includes one more section than the last one, please still refer to the previous "study guide" at the bottom of the Chapter 2.2 page.

Below are a few additional topics you should expect to see this time. Seek out relevant exercises on your own in both the Barron's book and our textbook.

• • Product Rule

  • Quotient Rule

  • Occasions when rewriting the function allows you to efficiently avoid the Product/Quotient rule (this is BIG DEAL!!!)
    Consult the “Right tool for the job” differentiation handout (including solutions) used in class. 

  • Free-fall motion questions that relate Position/Velocity/Acceleration