Answer
$\displaystyle \frac{dy}{dt}=( 100x^{99}-99x^{-2})\cdot\frac{dx}{dt}$
Work Step by Step
$x=x(t)$ so, by the chain rule,
$\displaystyle \frac{dy}{dt}=\frac{dy}{dx}\frac{dx}{dt}$
$\displaystyle \frac{dy}{dx}=(x^{100}+99x^{-1})^{\prime}=100x^{99}+99(-x^{-2})$
$= 100x^{99}-99x^{-2}$
$\displaystyle \frac{dy}{dt}=( 100x^{99}-99x^{-2})\cdot\frac{dx}{dt}$
