u=x^(2)+cos^(-1)(y)/(x)-y^(2)+tan^(-1)(x)/(y)=(del^(2)u)/(del x*del y)=(x^(2)-y^(2))/(x^(2)+y^(2))

If u = x ^ (2) tan ^ (- 1) ((y) / (x)) - y ^ (2) tan ^ (- 1) ((x) / (y)), prove that (del ^ (2) u) / (del x del y) = (x ^ (2) -y ^ (2)) / (x ^ (2) + y ^ (2))

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

If u=log(x^(2)+y^(2)+z^(2)) prove that (del^(2)u)/(del x^(2))+(del^(2)u)/(del y^(2))+(del^(2)u)/(del z^(2) = 2/(x^(2)+y^(2)+z^(2)

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

If u = x^(4) + y ^(3) + 3x ^(2) y^(2) + 3x ^(2) y find (del u)/(delx), (delu)/(dely), (del^(2) u)/(delx^(2)) , (del^(2)u)/(delx dely).

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

If u =x ^(2) + y ^(2) evaluate (del^(2)f)/(del x ^(2)) + (del ^(2) f)/(dy ^(2)):

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

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