## Thomas' Calculus 13th Edition

$\dfrac{s^5}{2}$ and $\dfrac{5ts^4}{2}$
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, $\dfrac{dw}{ds}=xy(2ts)+(\dfrac{x^2}{2})(\dfrac{1}{t})$ $\implies (ts^2)(\dfrac{s}{t})(2ts) +(ts^2)^2(2)(1/t)=\dfrac{5ts^4}{2}$