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If 2x2 + y2 = −2 then evaluate the second derivative of y with respect to x when x = 2 and y = 3. Round your answer to 2 decimal places. Use the hyphen symbol, -, for negative values.

If 2x2 y2 2 then evaluate the second derivative of y with respect to x when x 2 and y 3 Round your answer to 2 decimal places Use the hyphen symbol for negative class=
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Respuesta :

[tex]\bf 2x^2+y^2=-2\implies 4x+2y\cfrac{dy}{dx}=0\implies 2y\cfrac{dy}{dx}=-4x \\\\\\ \boxed{\cfrac{dy}{dx}=\cfrac{-2x}{y}}\\\\ -------------------------------\\\\ \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} \\\\\\ \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} \\\\\\ \boxed{-\cfrac{34}{27}}[/tex]

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