- State the chain rule for the composition of two functions.
- Apply the chain rule together with other rules.
- Recognize the chain rule for a composition of three or more functions.
- Chapter 3.6 The Chain Rule
- p. 297: 215, 221, 222, 229-237 odd
- Derivatives-Chain Rule
- Derivatives-Higher Order
Exit problems of the session
Find the derivative of the following functions:(a). (b). (c).
- Find the second order derivative for the given function .
- 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
- Chain rule introduction (5:06) Differentiate: .
- * Practice: Chain rule. (6 problems with a guiding text)
- Identifying composite functions (8:12) Find when and . Next, identify as the composition of functions. What about ? Is it a composition of functions?
- * Practice: Identify composite of functions. (4 problems)
- Derivative of using the chain rule. (9:16)
- Derivative of using the chain rule. (5:30)
- * Practice: Chain rule intro. (4 problems)
- Chain rule with table (2:26) For , find given the values of , , and when and .
- * Practice: Chain rule with tables. (4 problems)