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

If u =x ^(3) +2xy^(2) -x ^(2)y show that (del^(2)u)/(delxdely) =(del^(2)u)/(delydelx).

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

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

If u (x,y) = (x ^(2))/( y)- (2y ^(2))/(x) then (del^(2) u)/(del x dely) - (del ^(2) u)/(dely delx) is :

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 v(x,y,z) = x^(3) + y^(3) + z^(3) + 3xyz , show that (del^(2)v)/(del y del z) = (del^(2)v)/(del z del y)

If u=sin^(-1)((x+y)/(sqrtx+sqrty)) show that x(delu)/(delx)+y(delu)/(dely)=1/2 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 .

If u=x^2+3xy+y^2 Verify (del^2u)/(delxdely)=(del^2u)/(delydelx) .

If u =sqrt(x ^(4) +y ^(4)) show that x (delu)/(delx) + y ( del u)/(dely) =2u.