Math1011_Week07 - Math1011 Section 3.3 Differentiate the...

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Math1011 Section 3.3 10/4/2010 Differentiate the function 2 5 14 2 14.3 2 4 y x x π = + + + x
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Math1011 Section 3.3 1 Differentiate the function 2 5 14 2 14.3 2 4 y 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 7 5 13 2 5 ( ) 14 0 0 8 d dx 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 : [ ( ) ( )] ( ) ( ) 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 = = = + = + = (Doc #1011w.33.01)
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Math1011 Section 3.3 2 Differentiate the functions 5 4 2 2 3 17 y x x x = + 3 5 6 y x x = + + 2 4 2 y x π 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 3.3 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 = + + = = 2 4 2 y x π π π = + + 1 2 ' 4 0 0 Note: 2 and are constants y x π 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 #1011w.33.02)
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Math1011 Section 3.3 3 Differentiate the function 2 4 3 x x y x + + = 2 ( ) 4 ( ) f x x x x π = + +
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Math1011 Section 3.3 3 Differentiate the function y = x 2 + 4 x + 3 x 2 2 1.5 0.5 0.5 1.5 0.5 0.5 0.5 0.5 1.5 Simplify before taking the derivative 4 3 4 3 4 3 Now take the derivative ' 4 3 ' 1.5 2 1.5 d d d dx dx dx x x y x x x y x x x y x x x y x x x y x x x + + = = + + = + + = + + = + + − 2 ( ) 4 ( ) f x x x x π = + + 3 1.5 3 1.5 2 0.5 Distribute the 4x ( ) 4 4 4 Now take the derivative '( ) 4 4 4 '( ) 12 6 4 d d d dx dx dx f x x x x f x x x x f x x x π π π = + + = + + = + + (Doc #1011w.33.03)
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Math1011 Section 3.3 4 Differentiate 2 ( 2 ) ( ) y r r f = r 5 3 ( ) ( 1)(4 1) f t t t = + + 2 0 5 ( 1)( 7) d dx x x x x = + +
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Math1011 Section 3.3 4 Differentiate 2 ( 2 ) ( ) y r r f =
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