Answer
$\dfrac{s^5}{2}$ and $\dfrac{5ts^4}{2}$
Work Step by Step
Since, we have $\dfrac{dw}{dt}=\dfrac{dw}{dx}\dfrac{dx}{dt}+\dfrac{d w}{d y}\dfrac{dy}{dt}$
or, $\dfrac{dw}{dt}=xys^2+(x^2/2)(-s/t^2)=\dfrac{s^5}{2}$
and
$\dfrac{dw}{ds}=xy(2ts)+(x^2/2)(1/t)$
or, $=(ts^2)(s/t)(2ts) +(ts^2)^2(2)(1/t)$
and $\dfrac{dw}{ds}=\dfrac{5ts^4}{2}$
