Answer
$-500$
Work Step by Step
We have: $p=x^{0.5}y^{0.5}$
We need to differentiate both sides with respect to $x$.
$ \dfrac{dp}{dx}=\dfrac{d(x^{0.5}y^{0.5})}{dx}\\ - x^{-0.5} y^{0.5}=0.5y^{-0.5} x^{0.5} \dfrac{dy}{dx}\\ \dfrac{dy}{dx} =\dfrac{- y}{x} $
Plug the values in the given equation to obtain:
$ \dfrac{dy}{dx}=\dfrac{-(100000)}{200}=-500 $
