Mathematics - Differentiation Question with Solution | TestHub

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