Math1011_Week07

Math1011_Week07 - Math1011 Section 3.3 Differentiate the...

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Math1011 Section 3.3 10/4/2010 Differentiate the function 25 14 2 14.3 2 4 y xx π =+ + + x
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Math1011 Section 3.3 1 Differentiate the function 25 14 2 14.3 2 4 y xx π =+ + + x 75 2/5 2 5 ( ) : Power Rule with n = -2/5 d dx 14 13 ( ) : Power Rule with n = 14 14 (14.3) : Derivative of Constant 0 (2 ) : Derivative of Constant 0 22 ( 4 ) : Constant Multiple Rule 4 ( ) dd −⇒ 2 ( ) : Power Rule with n = 2 2 13 2 5 () 1 4 0 0 8 + + d dx 1 d dx dx dx d dx dx dx dx dx dx Derivative of a Constant Function: ( ) 0 Power Rule: ( ) Constant Multiple Rule: [ ( )] ( ) S u m R u l e : [() ] Difference Rule : [ ( ) ( )] ( ) ( ) nn c xn cf x f x fx gx d = = = += + −= (Doc #1011w.33.01)
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Math1011 Section 3.3 2 Differentiate the functions 542 23 1 7 y xxx =− + 3 56 yx x =+ + 2 42 ππ π + 3 1 e Find y’’(x) 43 2 7 xx + +
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Math1011 Section 3.3 2 Differentiate the functions 542 23 1 7 y xxx =− + 43 '5 8 6 0 + 3 56 yx x =+ + 2/3 1/2 5 1 32 1/3 3 '0 Note: x ; xx −− + == 2 42 ππ π + 1 2 '4 00 Note: 2 and are constants + 3 1 e 3 4 3 1 X '3 0 Note: ; is a constant xe + = Find y’’(x) 2 7 + + + 2 '8 9 2 7 '' 24 18 2 0 =++ + + (Doc #1011w.33.02)
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Math1011 Section 3.3 3 Differentiate the function 2 43 xx y x ++ = 2 () 4( ) fx 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 43 Now take the derivative '4 3 ' 1.5 2 1.5 ddd dx xx y x xxx yx −− ++ = =++ =+ + + + 2 () 4( ) fx π + 31 . 5 . 5 20 . 5 Distribute the 4x 4 4 4 Now take the derivative '( ) 4 4 4 '( ) 12 6 4 dd d + + + (Doc #1011w.33.03)
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Math1011 Section 3.3 4 Differentiate 2 (2 ) ( ) y rr f =− r 53 () ( 1 ) (4 1 ) ft t =+ + 2 0 5( 1 ) ( 7 ) d dx x xx = ++
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Math1011 Section 3.3 4 Differentiate 2 (2 ) ( ) y rr f =− r 2 22 2 Product Rule: (fg)'=fg'+gf' '( 2 ) ( ) 2 ) ( ( ) ) ( ) ( 2 ) 2 ) ' ( ) ( ) ( 2 2 ) dd dr yr fr rf + + 53 () ( 1 ) (4 1 ) ft t =+ + (5/2) (3/2) 2.5 0.5 1.5 1.5 3 2 2.5 0.5 1.5 1.5 Product Rule: (fg)'=fg'+gf' '( ) ( 1) (4 (4 ( '( ) ( 1)(4 ) 1)(2.5 ) '( ) ( 1)(6 ) 1)(2.5 ) dt + + + + + + + + i 2 0 5( 1 ) ( 7 ) d dx x xx = ++ 2 Product Rule: (fg)'=fg'+gf' ( 1 ) ( 7 ) ) ( 1 ) ( 7 ) ( 5 ) 5 [( ( 7) ( 7) ( 1)] ( 1)( 7)5 (5 )[( 1)(1) ( 7)(2 )] ( 1)( 7)5 (5 )( (5 )( 7)(2 ) ( 1)( 7)5 (5(0))(0 + + + + + + + + + + + + + + + + + + + + + 2 (5(0))(0 7)(2(0)) (0 1)(0 7)5 (0)(1) (0)(7)(0) (1)(7)(5) 35 +++ + + + = 2 (Doc #1011w.33.04)
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Math1011 Section 3.3 5 Differentiate y = t 2 3 t 2 2 t + 1 2 (1 ) (2 1 xx y ++ = )
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This note was uploaded on 12/06/2010 for the course MATH 1110 taught by Professor Martin,c. during the Fall '06 term at Cornell.

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Math1011_Week07 - Math1011 Section 3.3 Differentiate the...

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