[tex]\bf 2x^2+y^2=-2\implies 4x+2y\cfrac{dy}{dx}=0\implies 2y\cfrac{dy}{dx}=-4x
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\boxed{\cfrac{dy}{dx}=\cfrac{-2x}{y}}\\\\
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\cfrac{d^2y}{dx^2}=\cfrac{-2y-(-2x)\frac{dy}{dx}}{y^2}\implies \cfrac{d^2y}{dx^2}=\cfrac{2x\left( -\frac{2x}{y} \right)-2y}{y^2}
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\cfrac{d^2y}{dx^2}=\cfrac{\frac{-4x^2-2y^2}{y}}{y^2}\implies \left. \cfrac{d^2y}{dx^2}=\cfrac{-4x^2-2y^2}{y^3} \right|_{2,3}\implies \cfrac{-4(2)^2-2(3)^2}{(3)^3}
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\boxed{-\cfrac{34}{27}}[/tex]
