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posted by  h8calqlas on 8/24/2009 10:04:04 PM  |  status: Closed  |  Earned Karma: 285

Differentiation T

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If x2-2xy+3y2=8 then what is dy/dx?

Please use simple steps so that I can understand.
Tags: Calculus
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posted by Ramar on 8/24/2009 10:07:35 PM  |  status: Live
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                >>PRODUCT RULE<< FOR
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posted by velixy on 8/24/2009 10:07:56 PM  |  status: Live
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If x2-2xy+3y2=8 then what is dy/dx?
    2x -2y -2xy' +6 y y' =0
      2x-2y =  y' (2x-6y)        
                   y' = ( 2x-2y)(2x-6y)
                   y' = ( x-y)(x-3y)
dy/dx =   y' = ( x-y)(x-3y)  ANSWER
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posted by Mathtur on 8/24/2009 10:08:40 PM  |  status: Live
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Please read post and rate it accordingly.
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posted by Marth on 8/24/2009 10:25:42 PM  |  status: Live
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Use implicit differentiation: take the derivative with respect to x.

cancels out, leaving you with
 
Solve for






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posted by Altair on 8/24/2009 10:26:41 PM  |  status: Live
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x2-2xy+3y2=8
derivative both sides:
2x-2y-2xy'+6yy'=0
=>y' = (2y-2x)/(6y-2x)=(y-x)/(3y-x)
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posted by ayusuf on 8/24/2009 11:47:08 PM  |  status: Live
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Use implicit differentiation.
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posted by Kingle on 8/25/2009 3:01:17 AM  |  status: Live
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posted by Sonny's on 8/25/2009 1:35:13 PM  |  status: Live
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Use Implicit Differentiation Method.
Step #1: Differentiate both sides of the equation with respect to x.
Step #2: Collect all terms involving dy/dx on the left side of the equation and move all other terms to the right side of the equation.
Step #3: Factor dy/dx out of the left side of the equation.
Step #4: Solve for dy/dx by dividing both sides of the equation by (-2x+6y). Then factor out a -2 to the numerator and the denominator. The - 2 's cancel out.
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