Section_3_5Chain_Rule

# Section_3_5Chain_Rule - Section 3.5 Chain Rule Optional...

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Section 3.5 Chain Rule Optional Homework from the text: 3.5 #1-45 every other odd, 41,43,45,47,51,53,61,65,73 Chain Rule: Page 198, the rule is written out in the red box, F = f o g " F ( x ) = " f ( g ( x )) " g ( x ) or in Leibniz notation, y = f ( u ) u = g ( x ) dy dx = dy du du dx To verify the chain rule, lets again do one both way to show it works. Example f ( x ) = (3 x + 1) 2 1. First, multiply out and use power rule 2. Second, use the chain rule. 3. Verify they are the same. More Examples: Find the derivative of the following functions. a. y = sin(4 x 2 + 3) b. y = x 3 cos( a 2 + 3 x ) c. y = + 3 x + 5 x 3 Application to exponential functions with any base

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## This note was uploaded on 11/08/2011 for the course MA 141 taught by Professor Wears during the Spring '07 term at N.C. State.

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Section_3_5Chain_Rule - Section 3.5 Chain Rule Optional...

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