Mathematics - Differentiation Question with Solution | TestHub

Since, $$\begin{array}{rl}\Rightarrow \frac{d}{dy}\left(\frac{dx}{dy}\right)& =\frac{d}{dx}{\left(\frac{dy}{dx}\right)}^{-1}\frac{dx}{dy}\\ \frac{d^{2}x}{d{y}^2}& =-\left(\frac{d^{2}y}{d{x}^2}\right){\left(\frac{dy}{dx}\right)}^{-2}\left(\frac{dx}{dy}\right)\\ & =-\left(\frac{d^{2}y}{d{x}^2}\right){\left(\frac{dy}{dx}\right)}^{-3}\end{array}$$