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

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

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

If u=f(y/x) , then x(del u)/(del x) + y(del u)/(del y) =_________

If u=(x-y)^(2) , then (del u)/(del x) + (del u)/(del y) is

If v(x,y) = log((x^(2) +y^(2))/(x+y)) , prove that x(del v)/(del x) + y(del v)/(del y)=1 .

Ifu = sin ^ (- 1) ((x) / (y)) + tan ^ (- 1) ((y) / (x)), showthat x (u) / (x) + y (u ) / (del y) = 0

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 = 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)/(y)) show that (del^(2)u)/(delxdely) = (del^(2)u)/(delydelx) .