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Implicit Differentation

  1. Feb 14, 2009 #1
    1. The problem statement, all variables and given/known data
    find dy/dx for x2y+xy2=6


    2. Relevant equations



    3. The attempt at a solution
    d/dx (x2y+xy2) = d/dx (6)
    x2*(dy/dx)+y*2x+x*2y(dy/dx)+2y=0
    x2*(dy/dx)+y*2x+x*2y(dy/dx)=-2y
    (dy/dx)+y*2x+x*2y(dy/dx)=(-2y/x2)
    (dy/dx)+y*2x+(dy/dx)=(-2y/x2+2xy)

    I'm not sure what to do now, i know that the answer is (2xy-y2/x2+2xy)

    I got the denominator correct in my answer but i'm not sure how to get the numerator correctly. Did I go wrong somewhere during the process?
     
  2. jcsd
  3. Feb 14, 2009 #2

    Tom Mattson

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    Now you algebraically solve for dy/dx.
     
  4. Feb 14, 2009 #3
    Try that again. Piece by piece:
    [tex]x^2y[/tex] differentiates to [tex]2xy + x^2y'[/tex]
    [tex]xy^2[/tex] differentiates to [tex]y^2 + 2xyy'[/tex]

    Then follow Tom's advice!
     
  5. Feb 14, 2009 #4

    tiny-tim

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    Hi Jim4592! :smile:

    Isn't it (2xy + y2/x2+2xy)?
     
  6. Feb 14, 2009 #5
    Rather,

    -(2xy + y2)/(x2 + 2xy)
     
  7. Feb 14, 2009 #6

    tiny-tim

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    oops! :redface:

    thanks, Unco! :smile:
     
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