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$$\frac{d^2x}{dy^2}$$ equals
$$\left(\frac{d^2y}{dx^2}\right)^{-1}$$
$$-\left(\frac{d^2y}{dx^2}\right)^{-1}\left(\frac{dy}{dx}\right)^{-3}$$
$$\left(\frac{d^2y}{dx^2}\right)\left(\frac{dy}{dx}\right)^{-2}$$
$$-\left(\frac{d^2y}{dx^2}\right)\left(\frac{dy}{dx}\right)^{-3}$$
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