Second Derivative Using Implicit Differentiation

Question

If $$y$$ is a twice-differentiable function of $$x$$ such that $$x^2y + y^3 = 7$$, which of the following is an expression for $$\frac{d^2y}{dx^2}$$?

Accepted Answer

$$-\frac{2x + 3y^2 \cdot \frac{dy}{dx}}{x^2 + 3y^2}$$

Answer

$$-\frac{2x - 3y^2 \cdot \frac{dy}{dx}}{x^2 - 3y^2}$$

Answer

$$\frac{2x - 3y^2}{x^2 + 3y^2}$$

Answer

$$\frac{2x + 3y^2}{x^2 - 3y^2}$$

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