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2011 – Chain Rule

2011 – Chain Rule. AP CALCULUS. If you can’t do Algebra . . . . I guarantee you someone will do Algebra on you!. COMPOSITE FUNCTIONS. Know: Need: Know: Need: REM :. f(x)= 1.0825(x ). g(x)=.5(x). 10. 10. 20. f(x). COMPOSITE FUNCTIONS. g(x ) - what is done first. x.

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2011 – Chain Rule

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  1. 2011 – Chain Rule AP CALCULUS

  2. If you can’t do Algebra . . . . I guarantee you someone will do Algebra on you!

  3. COMPOSITE FUNCTIONS Know: Need: Know: Need: REM: f(x)=1.0825(x) g(x)=.5(x) 10 10 20

  4. f(x) COMPOSITE FUNCTIONS g(x) - what is done first. x Let and y = outside u = inside function function

  5. DECOMPOSE y = (outside) u = (inside). COMPOSITE FUNCTIONS

  6. Derivative of __________________________________________________ In Words: __________________________________________________________

  7. Chain Rule Leibniz Notation: In Words: __________________________________________________________

  8. Example 1: Example: Let y = u = _______

  9. Example 2:

  10. Example 3:

  11. Example 4: Example: Note:

  12. Example 6:

  13. Example 7: Extended Chain: Ex: OR WORDS: Extended Chain:___________

  14. Derivative of the Absolute Value Function REM: Do not simplify. Use the Chain Rule.

  15. General Rules: Working with number values Find the derivative. 1) f(x) + g(x) at x = 32) 2f(x) – 3g(x) at x =2 3) f(x)*g(x) at x = 24) f(x) / g(x) at x = 3 5) f(g(x)) at x = 26) (f(x))3 at x = 3

  16. Last Update • 10/13/07 • Assignment p. 153 # 13 – 31 odd, 56

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