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Implicit differentiation, find y''

  1. Sep 16, 2011 #1
    the problem is to find y'' or d2y / d2x

    the equation is y2 = x2

    first i found the first derivative dy/dx = 2x / 2y = x / y

    then i found the second using the quotient rule and got

    y'' = (y - x(dy/dx)) / y2

    i plugged in y' into y'' and got

    y'' = (y - (x2/y)) / y2

    but then im stuck after that because when i simplify i get
    y'' = (y2 - x2) / y3

    i dont know how i can plug the original equation back in.

    did i go wrong somewhere?
  2. jcsd
  3. Sep 16, 2011 #2


    Staff: Mentor

    This looks fine.
    This looks fine, too.
    This above is correct, but can be simplified. If y2 = x2, then y2 - x2 = ?
  4. Sep 16, 2011 #3


    User Avatar
    Homework Helper

    Take care, you have to exclude x=y=0.
    The original equation is y2=x2. What do you get when you plug that in?

  5. Sep 16, 2011 #4
    does x2-y2 = 0 or 1?

    and the book shows that the answer is 3y/4x2 = 3x / 4y, hows that possible? shouldnt the answer be y'' = ......?
  6. Sep 16, 2011 #5


    Staff: Mentor

    If two numbers are equal, then subtracting one from the other leaves zero.
    Yes, they're asking you for y'', so the answer should start with y'' = ...

    I don't see how they got 3y/4x2 = 3x / 4y.

    Going back to the original problem, you have y2 = x2, which is equivalent to two equations: y = x or y = -x. For the first, y' = 1, and for the second, y' = -1. What do these tell you about y''?
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