Answer
$\frac{dx}{dt} = 55$
Work Step by Step
Given that $\frac{dy}{dt} = 5$ and $x=y^3-y$
on differentiating with respect to time
$\frac{dx}{dt}$ = $\frac{d (y^3-y)}{dt}$
$\frac{dx}{dt} = \frac{3y^2dy}{dt}-\frac{dy}{dt}$
when y=2
then $ \frac{dx}{dt} = 3\times (4)\times5-5$
Thus, the answer is $\frac{dx}{dt} = 55$
