2011 – Chain Rule AP CALCULUS. If you can’t do Algebra.... I guarantee you someone will do Algebra on you!

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Presentation transcript:

2011 – Chain Rule AP CALCULUS

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

COMPOSITE FUNCTIONS Know:Need: REM : 2010 f(x)=1.0825(x) g(x)=.5(x)

COMPOSITE FUNCTIONS Let and y = outsideu = insidefunction g(x) - what is done first. f(x) x

COMPOSITE FUNCTIONS DECOMPOSEy = (outside)u = (inside).

In Words: __________________________________________________________ Derivative of __________________________________________________

Chain Rule Leibniz Notation: In Words: __________________________________________________________

Example 1: Example: Let y = u = _______

Example 2:

Example 3:

Example 4: Example: Note:

Example 6:

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

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

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 x f(x) g(x) f / (x) g / (x)

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