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2.4

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

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2.4

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  1. Photo by Vickie Kelly, 2002 Greg Kelly, Hanford High School, Richland, Washington The Chain Rule 2.4

  2. Photo by Vickie Kelly, 2002 Greg Kelly, Hanford High School, Richland, Washington U.S.S. Alabama Mobile, Alabama

  3. 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.

  4. 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.

  5. Consider a simple composite function:

  6. and another:

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

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

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

  10. Example: Find the derivative

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

  12. 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

  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. Example: Find the derivative

  19. Homework 2.4 (page133) #7-41 odd

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