#### Answer

See the answer below.

#### Work Step by Step

Implicitly differentiating $xy=1$ with respect to $t$, we have
$\frac{dx}{dt}\times y+ x\frac{dy}{dt}=0$
$\implies x \frac{dy}{dt}=-y\frac{dx}{dt}$
$\implies \frac{dy}{dt}=-\frac{y}{x}\frac{dx}{dt}$