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

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

If w(x,y) = xy + sin(xy) , then prove that (del^(2) w)/(del y del x) = (del^(2) w)/(del x del y)

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

If u=log (x^(3) + y^(3) +z^(3) - 3xyz) , then (del u)/(del x) + (del u)/(del y) + (del u)/(del z)=

If u= x^3-3xy^2 , show that (del^2u)/(delx^2)+(del^2u)/(dely^2) =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 z (x + y) = x ^ (2) + y ^ (2) show that [(del z) / (del x) - (del z) / (del y)] ^ (2) = 4 [1 - (del z) / (del x) - (del z) / (del y)]

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