Prove that ∂z/∂r + ∂z/∂s = 0

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x=r-s, y=s-r, ∂x/∂r=1, ∂x/∂s=-1, ∂y/∂s=1, ∂y/∂r=-1.

∂z/∂r=(∂z/∂x)(∂x/∂r)=∂z/∂x, ∂z/∂r=(∂z/∂y)(∂y/∂r)=-∂z/∂y;

∂z/∂s=(∂z/∂x)(∂x/∂s)=-∂z/∂x, ∂z/∂s=(∂z/∂y)(∂y/∂s)=∂z/∂y.

Therefore, ∂z/∂r+∂z/∂s=∂z/∂x-∂z/∂x=-∂z/∂y+∂z/∂y=0.

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