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