Question

Xy=1 for x=2, dx/dt= -2 find dy/dt

Answer 1

`\bf xy=1\iff y = \cfrac{1}{x}\iff y = x^(-1)\\\\ -----------------------------\\\\ \cfrac{dy}{dt}=-x^(-2)\cdot \cfrac{dx}{dt}\impliedby \textit{using the chain-rule} \\\\\\ \left. \cfrac{dy}{dt}=-\cfrac{(dx)/(dt)}{x^2} \right|{ \begin{array}{llll} x=2\\ (dx)/(dt)=-2 \end{array}}\implies \cfrac{dy}{dt}=-\cfrac{-2}{2^2}`