[tex]\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}[/tex]
