Chapter 3 Section 03

# Chapter 3 Section 03 - 3.3 Product and Quotient Rules page...

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1 3.3 Product and Quotient Rules page 143

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2 Consider the following: D x [(x - 1)(x - 2)] = D x [x 2 – 3x + 2] = 2x – 3 but, D x [x-1] = 1 and D x [x-2] = 1 so, D x [x-1]∙D x [x-2] = 1 Derivative of a product is NOT the product of the derivatives
3 And… [ ] [ ] [ ] [ ] [ ] s. derivative the of quotient the NOT is quotient a of derivative The 2 2 1 2 2 1 1 2 1 1 2 2 1 2 1 1 1 ) 1 )( 1 ( 1 1 2 2 2 2 - = - = - + - = - - = + - = - = - - - = - + - x x x dx d x x dx d so x dx d and x x x dx d but x dx d x x x dx d x x x dx d

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4 Objectives 1. Prove the product rule and use it to find the derivatives of products of functions. 2. Prove the quotient rule and use it to find the derivatives of quotients of functions. 3. Determine when the product and quotient rules should be used and when it is easier to simplify.
5 Product Rule D x [f(x)∙g(x)] = f(x)∙g’(x) + g(x)∙f’(x) [ ] [ ] x e e x x g x dx d e e dx d x x g e x x g Example x x x x x 2 1 + = + = = ) ( ' ) ( ' ) ( :

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## This note was uploaded on 09/28/2009 for the course MATH 1550 taught by Professor Wei during the Spring '08 term at LSU.

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Chapter 3 Section 03 - 3.3 Product and Quotient Rules page...

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