Section 3 3 notes

# Section 3 3 notes - = [ ] x x dx d 2 csc cot-= [ ] x x x dx...

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Section 3.3 The Product and Quotient Rules and Higher-Order Derivatives

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The Product Rule Note: The derivative of a product is NOT the product of the derivatives. NO PARTIAL CREDIT for committing this no-no. ) ( ' ) ( ) ( ' ) ( )] ( ) ( [ x f x g x g x f x g x f dx d + =
Examples: #4 #14 C=1 ( 29 2 4 ) ( s s s g - = ) 1 )( 1 2 ( ) ( 3 2 - + - = x x x x f

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The Quotient Rule Aka lo ‘d hi minus hi ‘d lo over lolo Note: The derivative of a quotient is NOT the quotient of the derivatives and NO PARTIAL credit will be awarded for this no-no. [ ] 2 ) ( ) ( ' ) ( ) ( ' ) ( ) ( ) ( x g x g x f x f x g x g x f dx d - =
Examples: #8 #44 7 2 2 ) ( 2 - + = t t t g x x x f sin ) ( =

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Trigonometric Derivatives From the quotient rule we get: MEMORIZE THEM [ ] x x dx d 2 sec tan

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Unformatted text preview: = [ ] x x dx d 2 csc cot-= [ ] x x x dx d tan sec sec = [ ] x x x dx d cot csc csc-= Examples: #53 #72 (0, ) x x x f tan ) ( 2 = 4 ) ( + = x e x f x Higher Order Derivatives Second Derivative Notations For higher than second, you will have analogous notations. See the listing on page 146 of your text. ' ' y ) ( ' ' x f 2 2 dx y d [ ] ) ( 2 2 x f dx d More examples #78 Determine the points at which the graph of the function has a horizontal tangent line. #88, 98, 108 1 ) ( 2 2 + = x x x f...
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## This note was uploaded on 01/13/2012 for the course MATH 2554 taught by Professor Pamelasatterfield during the Spring '11 term at NorthWest Arkansas Community College.

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Section 3 3 notes - = [ ] x x dx d 2 csc cot-= [ ] x x x dx...

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