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Math1011_Week05_3_23

Math1011_Week05_3_23 - Math1011 Section 3.2 Differentiate...

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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
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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 0 d dx (2 ) : Derivative of Constant 0 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 | | ( ) 14 0 0 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: ( ) 0 Power Rule: ( ) Constant Multiple Rule: [ ( )] ( ) Sum Rule: [ ( ) ( )] ( ) ( ) Difference Rule : [ ( ) ( )] ( ) ( ) Der n n c x nx 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)
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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
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Math1011 Section 3.2 2 Differentiate the functions 5 4 2 2 3 17 y x x x = + 4 3 ' 5 8 6 0 y x x x = + 3 5 6 y x x = + + 2/3 1/2 5 1 3 2 1/3 1/2 3 ' 0 Note: x ; y x x x x x = + + = = 4 2 |4 | y x x π π = + + 1 | | ' 4 0 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 0 Note: ; is a constant y x x e π = − + = Find y’’(x) 4 3 2 2 3 7 y x x x = + + + x + 3 2 2 ' 8 9 2 7 '' 24 18 2 0 y x x x y x x = + + + = + + (Doc #011w.32.02t)
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Math1011 Section 3.2 3 Differentiate the function 2 4 3 x x y x + + = 2 ( ) 4 ( ) f x x x x π = + +
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