Answer
$-3000 $
Work Step by Step
We have: $p=x^{0.6}y^{0.4}$
We need to differentiate both sides with respect to $x$.
$ -0.6 x^{-0.4} y^{0.4} \dfrac{dy}{dx}=0.4 y^{0.6} x^{0.6}\dfrac{dy}{dx} \\ \dfrac{dy}{dx}=\dfrac{-3 y}{2x} $
Plug the values in the given equation to obtain:
$ \dfrac{dy}{dx}=\dfrac{-3 (200000)}{2(100)}=-3000 $
