Question

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

Answer 1

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