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show me how to solve this problem: (xy)^2=2x+9y^2 implicit diff...

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please help!

asked Feb 28, 2014 in CALCULUS by abstain12 Apprentice

1 Answer

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x y ) 2 = 2 x + 9 y 2

Derivitive each term with respected to x.

d / d x ( x y ) 2 = d / d x ( 2 x ) + d / d x ( 9 y 2)

2 ( x y )  d / d x ( x y ) = 2 + 9 * 2 y ( d y / d x )

Apply the prodect property  d / d x ( u v ) = u v ' + v u '

2 ( x y )  [ x  d y / d x + y d x / d x ) = 2 + 18  y ( d y / d x )

2 ( x y )  [ x  d y / d x + y * 1) = 2 + 18  y ( d y / d x )

x2 y  d y / d x + 2 x y2  = 2 + 18  y ( d y / dx )

x2 y  d y / d x - 18  y ( d y / d x ) = 2 - 2 x y2 

[ 2  x2 y - 18  y ] ( d y / d x ) = 2 ( 1 -  x y2 )

2y [   x2  - 9  ] ( d y / d x ) = 2 ( 1 -  x y2 )

y [   x2  - 9  ] ( d y / d x ) =  ( 1 -  x y2 )

( d y / d x ) =  ( 1 -  x y2 ) / y [   x2  - 9  ]

Therefore  ( d y / dx ) =  ( 1 -  x y2 ) / y [   x2  - 9  ]. 

answered Apr 4, 2014 by friend Mentor

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