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AP Calc

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

  • AP Calc -

    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.
    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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