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The Chain Rule

The Chain Rule. Section 2.4. After this lesson, you should be able to:. 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 using algebra.

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The Chain Rule

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  1. The Chain Rule Section 2.4

  2. After this lesson, you should be able to: • 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 using algebra. • Find the derivative of a trigonometric function using the Chain Rule.

  3. or, The Chain Rule To find the derivative of the composition of functions. If f(u) is a differentiable function of u and u = g(x) is a differentiable function of x, then y = f(g(x)) is a differentiable function of x and

  4. (power rule) (extended power rule) Extended Power Rule

  5. Example Example*: Find the derivative

  6. Example

  7. Example

  8. Example Using the Chain Rule w/ the Quotient Rule

  9. Example

  10. Example

  11. Example

  12. Example

  13. Find the derivative of and Example

  14. Example

  15. More Trig Derivatives…

  16. Example Using the chain rule twice.

  17. Homework Section 2.4 page 137 #7-27 odd, 41-57 odd, 61, 67, 71, 73, 85, 111

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