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2010 – Chain Rule

2010 – 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 :. t (x )= 1.0825(x ). Order matters. d (x )=.5(x). 10.83. 10. Shirt for $20. 10. 20. f(x). COMPOSITE FUNCTIONS.

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2010 – Chain Rule

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  1. 2010 – 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: t(x)=1.0825(x) Order matters d(x)=.5(x) 10.83 10 Shirt for $20 10 20

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

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

  6. Derivative of __________________________________________________ a composite function 2 functions 2 parts Texas two step In Words: __________________________________________________________ d(outside)leave the inside alone*d(inside)

  7. Chain Rule Leibniz Notation: In Words: __________________________________________________________ d(outside)leave the inside alone*d(inside)

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

  9. Example 2: Two steps:

  10. Example 3:

  11. Example 4: Example: Note:

  12. Example 6:

  13. Example 7: d(outside)*d(middle)*d(inside) Extended Chain: Ex: OR WORDS: Extended Chain:___________ Number of functions = number of parts

  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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