z=(x+y)/(x-y)
= 1 + 2y/(x-y)
∂z/∂x = -2y/(x-y)^2
∂^2z/∂x^2 = 4y/(x-y)^3
∂^2z/∂x∂y
= -2[(x-y)^2+ 2y(x-y) ]/(x-y)^4
=-2[(x-y)+ 2y ]/(x-y)^3
=-2(x+y)/(x-y)^3
z=(x+y)/(x-y)
=-1 +x/(x-y)
∂z/∂y = x/(x-y)^2
∂^2z/∂y^2 = 2x/(x-y)^3
∂^2z/∂y∂x
=[(x-y)^2 - 2x(x-y) ]/(x-y)^4
=[(x-y) - 2x ]/(x-y)^3
=-(x+y)/(x-y)^3
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