αz/αx=αz/αu*αu/αx+αz/αv*αv/αx
αz/αy=αz/αu*αu/αy+αz/αv*αv/αy
αz/αu=v,αz/αv=u
αu/αx=2,αv/αx=1
αu/αy=1,αv/αy=-2
∴αz/αx=αz/αu*αu/αx+αz/αv*αv/αx
=v*2+u*1=2v+u
=2(x-2y)+(2x+y)
=4x-3y
∴αz/αy=αz/αu*αu/αy+αz/αv*αv/αy
=v*1+u*(-2)=v-2u
=(x-2y)-2(2x+y)
=-3x-4y