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Posted by on Tuesday, November 6, 2012 at 10:31am.

I need to find the second derivative for this:
2x^2-3y^2=4
I understand all the steps but for some reason I get the wrong numerator. I get
(6y^-4x^2)/9y^3
The answer is -8/9y^3

  • AP Calc - , Tuesday, November 6, 2012 at 11:00am

    You did just fine and your second derivative is correct, if you meant (6y^2 - 4x^2)/(9y^3)
    except they took it a bit further.

    notice your numerator is
    -4x^2 + 6y^2

    from the original
    2x^2 - 3y^2 = 4 , then
    4x^2 - 6y^2 = 8 , and
    -4x^2 + 6y^2 = -8

    to get their -8/9y^3

    If you were marked "wrong", then that is bad,
    when differentiating implicitly, there are often multiple variations of the same answer.

    Here is a way to check if two possible answers are equivalent:
    Pick any point which satisfies the original equation, sub that point into the two variations of the derivatives, you should get the same answer if they are equivalent.
    e.g.
    the point (√8,2) is on the original curve
    y'' -- your answer -- = (24 - 32)/72 = -8/72 = -1/9
    y'' -- their answer = -8/72 = -1/9

    ok, then !!

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