1. U.S.S. Alabama 2.4 Chain Rule Mobile, Alabama
Greg Kelly, Hanford High School, Richland, Washington
Photo by Vickie Kelly, 2002

2. 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.

3. We now have a pretty good list of “shortcuts” to find derivatives of simple functions.
Of course, many of the functions that we will encounter are not so simple. What is needed is a way to combine derivative rules to evaluate more complicated functions.

4. Consider a simple composite function:

5. and another:

6. and one more:
This pattern is called the chain rule.

7. Chain Rule:
If is the composite of and , then:

8. Chain Rule:
If is the composite of and , then:
Proof:

9. Example: Find the derivative

10. General Power Rule:
Derivative formulas include the chain rule!

11. Every derivative problem could be thought of as a chain-rule problem:
The most common mistake on this test is to forget to use the chain rule.
Every derivative problem could be thought of as a chain-rule problem:
The derivative of x is one.
derivative of outside function
derivative of inside function

12. Example: Find the derivative

13. Example: Find the derivative

14. Example: Find the derivative

15. Example: Find the derivative

16. Example: Find the derivative

17. Example: Find the derivative

18. Homework
2.4 (page 137)
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