Chapter 2.4 - The Chain Rule

Objectives:

• Find the derivative of a composite function using the Chain Rule.
• Find the derivative of a function using the General Power Rule.
• Simplify the derivative of a function using algebra.
• Find the derivative of a trigonometric function using the Chain Rule.

Chain Rule pt1 (for Day #9 lesson)

Introduction to the chain rule, for deriving composite functions (i.e. functions plugged into other functions)

Chain Rule pt2 (for Day #9 & #10 lesson)

Chain rule used along with product or quotient rule. Juggling all the expressions and making sure you apply the rules in the correct order is part of the challenge.

Chain Rule pt3 (for Day #10 lesson)

Chain rule involving trigonometric functions.

Product/Quotient/Chain Exercises

Finding derivatives that involve a combination of rules such as Product Rule, Quotient Rule, and Chain Rule in addition to all the basic derivative rules (Power, Trig, Constant, Constant Multiple, etc.) often proves particularly challenging to students. This is a skill you must learn to master in order to succeed in upcoming topics, and this type of question will appear over and over on upcoming assessments. Here are a few additional exercises for this topic, with full solutions worked out on the second page.

In class I've probably started using the term "critical number" to refer to the solutions for the equation f'(x) = 0 or undefined. This term is officially introduced in Chapter 3.1.

Go to next page, Chapter 2.5.