Math1011_Week09_Prelim2B - Math1011 - Learning Strategies...

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Unformatted text preview: Math1011 - Learning Strategies Center Various Prelims II-B1 2 3 The equation x 11 defines the following curve: xy y + + = Find the equation of the tangent line at (1, 2). dy dx Find if sin 1 x x y y e + = Math1011 Various Prelims B1 2 3 The equation x 11 defines the following curve: xy y + + = Find the equation of the tangent line at (1, 2). 2 2 2 3 d d d d dx dx dx dx 2 d dx 2 2 2 3 2(1) (2) 4 1 (1) 3(2) Implicit Differentiation: (x ) ( ) ( ) (11) 2 ' 3 ' 0 Note: Use product rule for ( ) xy'+3y ' 2 '( 3 ) 2 ' at point (1, 2): ' x y x y xy y x x y y y y x y y x y y x y x y y y − − + − − − + + + = + + + = = − − + = − − = = = 3 4 13 Equation of Tangent Line: ( - ) (- ) ( -2) ( 1) y y m x x y x − = ⇒ = − dy dx Find if sin 1 x x y y e + = d d d dx dx dx d d d d dx dx dx dx Implicit Differentiation ( sin ) ( ) (1) (sin ) sin ( ) ( ) ( ) cos ' sin (1) ( ) ' cos ' ' sin '( cos ) sin sin ' cos x x x x x x x x x x x x y y e x y y x y e e y x y y y y e e y x y y e y y y e y x y e y ye y y e y x y e + = + + + = + + + = + = − − + = − − − − = + (Doc #011p.36.01t)(Spring 2005/Fall1999) Math1011 - Learning Strategies Center Various Prelims B2 dy dx Find if x 1 y + = dy 2 dx Find if ( 1) x y x + = + dy dx Find if sin x cos 1 y + = Math1011 Various Prelims B2 dy dx Find if x 1 y + = 1/2 1/2 d d d dx dx dx 1/2 1/2 1 1 2 2 1 1 2 x 2 y 1-1 2 y 2 x-2 y- y 2 x x ( ) ( ) (1) Implicit Differentiation ' ' ' ' x y x y y y y y − − + = + = + = = = = dy 2 dx Find if ( 1) x y x + = + 2 d dx dy 1 y dx dy 1 1 y 1 dx dy 2 1 dx dy 2 2 1 dx ln ln( 1) ln ( 2)ln( +1) (ln ) (( 2)ln( +1)) ( 2 ) ( l n ( + 1 ) ) l n ( + 1 ) ( 2 ( 2 ) l n ( + 1 ) [ l n ( + 1 ) ] ( 1 ) [ l n ( + 1 ) ] x d dx d d dx dx x x x x x x ) y x y x x y x x x x x x x x y x x x + + + + + + + = + = + = + = + + + = + + = + = + + dy dx Find if sin x cos 1 y + = 1/2 1/2 d d d dx dx dx 1/2 1/2 1 1 2 2 1 1 2 x 2 y sin-cos 2 y 2 x 2 y cos 2 y y cos-cos 2 x sin sin 2 x x sin Implicit Differentiation (sin ) (cos ) (1) cos sin ' cos sin ' ' ' y x x x x y y y x y x x y y y x y y y y − − − ⋅ − ⋅ + = ⋅ + − ⋅ ⋅ − ⋅ = = = ⋅ = = = (Doc #011p.36.02t)( Fall2003)(Spring 2006) Math1011 Spring 2007/Fall 2007...
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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_Week09_Prelim2B - Math1011 - Learning Strategies...

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