I have this question in my question bank
With usual notation ,$\frac{d^{2}x}{dy^{2}}$ is $$\begin{align} &1)\left(\frac{d^{2}y}{dx^{2}}\right)^{-1}\\ &2)\frac{d^{2}y}{dx^{2}}\left(\frac{dy}{dx}\right)^{-2}\\ &3)-\left(\frac{d^{2}y}{dx^{2}}\right)^{-1}\left(\frac{dy}{dx}\right)^{-2}\\ &4)\left(\frac{d^{2}y}{dx^{2}}\right)\left(\frac{dy}{dx}\right)^{-3}\\ \end{align}$$
I do not understand how to represent second order derivative in one of the given forms. This HINT is also provided with the question: $\left(\frac{dx}{dy}\right)=\left(\frac{dy}{dx}\right)^{-1}$ now differentiate both side wrt $y$ if somehow it is correct to differentiate then I got stuck here $=-1\left(\frac{dy}{dx}\right)^{-2}\cdot \frac{d}{dy}\left(\frac{dy}{dx}\right)$ applied chain rule. If I again use there inverse of derivative technique I'll get what I started with, I want to know is it a correct question? and are there such usual notations?, thanks
