Answer
$\frac{\partial w}{\partial r}=2$
$\frac{\partial w}{\partial s}=2-\pi$
Work Step by Step
$x=r+sin(s)=\pi$ when $r=\pi, s=0$
$\frac{dx}{dr}=1, \frac{dx}{ds}=cos(s)=1$ when $r=\pi, s=0$
$y=rs=0$ when $r=\pi, s=0$
$\frac{dy}{dr}=s=0, \frac{dy}{ds}=r=\pi$ when $r=\pi, s=0$
$w=sin(2x-y)=0$ when $r=\pi, s=0$
$\frac{dw}{dx}=2cos(2x-y)=2, \frac{dw}{dy}=-cos(2x-y)=-1$ when $r=\pi, s=0$
$\frac{\partial w}{\partial r}=\frac{dw}{dx}\frac{dx}{dr}+\frac{dw}{dy}\frac{dy}{dr}=2\times1-1\times0=2$ when $r=\pi, s=0$
$\frac{\partial w}{\partial s}=\frac{dw}{dx}\frac{dx}{ds}+\frac{dw}{dy}\frac{dy}{ds}=2\times1-1\times\pi=2-\pi$ when $r=\pi, s=0$
