Answer
$-125 $
Work Step by Step
We have: $xy-2000=y$
Now, $at x=5$, we have: $5y-2000=y \implies y=500$
We need to differentiate both sides with respect to $x$.
$ x\dfrac{dy}{dx}+y-0=\dfrac{dy}{dx} \\ (x-1) \dfrac{dy}{dx}=-y\\ \dfrac{dy}{dx} =\dfrac{- y}{(x-1)} $
Plug the values in the given equation to obtain:
$ \dfrac{dy}{dx}=\dfrac{-500}{4}=-125 $
