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Second derivative of the equation for an elipse.

  1. Oct 3, 2012 #1
    1. The problem statement, all variables and given/known data
    Determine the second derivative of y with respect to x when 2x2+3y2=0

    2. Relevant equations
    possible answers include:
    2/(3y2)
    -2/(9y3)
    2/(3y3)
    -2/(3y2)
    -2/(3y3)


    3. The attempt at a solution

    I took the first derivative with respect to x implicitly and came up with
    -2x/3y

    I then took the second derivative, but here's where I get stuck.
    I wind up with:
    (-2y+2x(y'))/(3y^2)

    The only possible answers have only y in them, while I see no way to get rid of x in my solution. I've done this several times and come up with the same answer each time, what am I doing wrong?
     
  2. jcsd
  3. Oct 3, 2012 #2

    vela

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    Use the equation for the ellipse to eliminate x.
     
  4. Oct 3, 2012 #3

    SammyS

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    Did you plug your result for y' into you result for y": y" = (-2y+2x(y'))/(3y2)
     
  5. Oct 4, 2012 #4
    Yes I did,but you'll notice that still doesn't get rid of x.

    Vela, what do you mean by that?
     
  6. Oct 4, 2012 #5

    vela

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    Oh, sorry, it's not an equation of an ellipse. You can use the original equation ##2x^2+3y^2=0## to solve for ##x## in terms of ##y##.
     
  7. Oct 4, 2012 #6

    SammyS

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    What did you get when you plugged your result for y' into your result for y": y" = (-2y+2x(y'))/(3y2) ?
     
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