Math1011_Week05_3_23 - Math1011 Section 3.2 9/30/2009...

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Unformatted text preview: Math1011 Section 3.2 9/30/2009 Differentiate the function 2 5 14 2 14.3 2 4 |5 | y x x x π − = + + + − + x Math1011 Section 3.2 9/30/2009 Differentiate the function 2 5 14 2 14.3 2 4 |5 | y x x x π − = + + + − + x 7 5 2/5 2 5 ( ) : Power Rule with n = -2/5 d dx x x − − − ⇒ 14 13 ( ) : Power Rule with n = 14 14 d dx x x ⇒ (14.3) : Derivative of Constant d dx ⇒ (2 ) : Derivative of Constant d dx π ⇒ 2 2 ( 4 ) : Constant Multiple Rule 4 ( ) d d dx dx x x − ⇒ − 2 ( ) : Power Rule with n = 2 2 d dx x x ⇒ | | | |: Absolute Value Rule d x dx x x ⇒ 7 5 13 5 2 5 | | ( ) 1 4 8 d x dx x y x x x − − = + + + − + d dx 1 d dx d d dx dx d d d dx dx dx d d dx dx dx Derivative of a Constant Function: ( ) Power Rule: ( ) Constant Multiple Rule: [ ( )] ( ) Sum Rule : [ ( ) ( )] ( ) ( ) Difference Rule : [ ( ) ( )] ( ) ( ) Der n n c x n x cf x c f x f x g x f x g x f x g x f x g x − d = = = + = + − = − d dx | | ivative of Absolute Value: | | x x x = (Doc #011w.32.01t) Math1011 Section 3.2 2 Differentiate the functions 5 4 2 2 3 17 y x x x = − + − 3 5 6 y x x = + + 4 2 | 4 | y x x π π = + + 3 1 x y e π = + Find y’’(x) 4 3 2 2 3 7 y x x x = + + + x Math1011 Section 3.2 2 Differentiate the functions 5 4 2 2 3 17 y x x x = − + − 4 3 ' 5 8 6 y x x x = − + − 3 5 6 y x x = + + 2/3 1/2 5 1 3 2 1/3 1/2 3 ' Note: x ; y x x x x x − − = + + = = 4 2 | 4 | y x x π π = + + 1 | | ' 4 4 Note: 2 is a constant,| 4 | 4| | x x y x x x π π π − = + + = 3 1 x y e π = + 3 4 3 1 X ' 3 Note: ; is a constant y x...
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This note was uploaded on 11/22/2009 for the course CHEM 2070 at Cornell University (Engineering School).

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Math1011_Week05_3_23 - Math1011 Section 3.2 9/30/2009...

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