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If $\frac{d^{2} x}{{dy}^{2}} = \frac{- \frac{d^{2} y}{{dx}^{2}}}{{(\frac{dy}{dx})}^{n}}$ then $n =$

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3

$\frac{d x}{d y} = \frac{1}{\frac{dy}{dx}} = {(\frac{dy}{dx})}^{- 1}$
Differentiate w.r.t ‘ y ’
$\begin{array}{rcl} \frac{d^{2} x}{{dy}^{2}} & = & - {(\frac{d y}{d x})}^{- 2} \frac{d}{d y} (\frac{d y}{d x}) \\ = & - {(\frac{d y}{d x})}^{- 2} \frac{d^{2} y}{d x^{2}} \frac{d x}{d y} \\ = & - \frac{\frac{d^{2} y}{d x^{2}}}{{(\frac{d y}{d x})}^{3}} \end{array}$
we get $n = 3$

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