" If "u=sin^(-1)(x)/(y)+tan^(-1)(y)/(x)," show that "x(del u)/(del x)+y(del u)/(del y)=0

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If u = sin ^(-1) ((x ^(3) + y ^3)/(x-y)) show that x (del u)/(delx) + y (del u )/(del y) = 2 tan u.

If u= tan^(-1) ((x^(3) + y^(3))/(x-y)) , Prove that x(del u)/(del x) + y(del u)/(del y) = sin 2u .

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If u(x,y) = (x^(2) + y^(2))/sqrt(x+y) , prove that x(del u)/(del x) + y(del u)/(del y) = 3/2 u .

If u = cos ^(-1) ((x)/(y)) prove that x (del u)/(delx) + y (del u)/(dely)=0.

If u =tan^(-1)((x)/(y)) show that (del^(2)u)/(delxdely) = (del^(2)u)/(delydelx) .

If u=(x^(2)+y^(2)+z^(2))^(-1/2) show that x(del u)/(del x)+y(del u)/(del y)+z(del u)/(del z)=-u