Learning Outcomes

1. State the chain rule for the composition of two functions.
2. Apply the chain rule together with other rules.
3. Recognize the chain rule for a composition of three or more functions.

Textbook

• Chapter 3.6   The Chain Rule

Textbook Assignment

• p. 297:    215, 221, 222, 229-237 odd

WeBWork Assignment

• Derivatives-Chain Rule
• Derivatives-Higher Order

Exit problems of the session

1. Find the derivative of the following functions:

(a). (b). (c). 2. Find the second order derivative for the given function .

Key Concepts

• The chain rule allows us to differentiate compositions of two or more functions. It states that for , In Leibniz’s notation, this rule takes the form: • The chain rule can be combined with other rules we have learned. For example combining the chain rule with the power rule gives: or in Leibniz’s notation: #### Videos and Practice Problems of Selected Topics

1. Chain rule introduction  (5:06) Differentiate: .
2. * Practice: Chain rule. (6 problems with a guiding text)
3. Identifying composite functions (8:12) Find when and . Next, identify as the composition of functions. What about ? Is it a composition of functions?
4. * Practice: Identify composite of functions. (4 problems)
5. Derivative of using the chain rule. (9:16)
6. Derivative of using the chain rule. (5:30)
7. * Practice: Chain rule intro. (4 problems)
8. Chain rule with table (2:26) For , find given the values of , , and when and .
9. * Practice: Chain rule with tables. (4 problems)