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First and Second Derivatives : Using Implicit Differentiation

X^2y^2-2x=3

I'm trying to verify my answer for the first derivative, and see if I got the second one right as well. For the first derivative I got
(1-xy^2)/(x^2y)
I think I'm having a problem with the 2nd derivative because I got
x^2-2x^3y^2+x^3y^4
It doesn't look right to me, so I'd like to figure out where I went wrong by looking at the steps.

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Implicit differentiation is investigated.

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