If `u=(x^2y^2)/(x+y)` , show that `x(del^2u)/(delx^2)+y(del^2u)/(delydelx)=(delu)/(delx)`

If u = (x^2+y^2+z^2)^(-1/2) then prove that (del^2u)/(delx^2)+(del^2u)/(dely^2)+(del^2u)/(delz^2) =0

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=(y)/(z)+(z)/(x), then find x(del u)/(del x)+y(del u)/(del y)+z(del u)/(del z) .

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 y=f(x+ct)+g(x-ct), then show that (del^(2)y)/(del t^(2))=c^(2)(del^(2)y)/(del x^(2))

If H=f(y-z,z-x,x-y) Prove that (del H)/(del x)+(del H)/(del y)+(del H)/(del z)=0

If u=x^y then find (del u)/(del x) and (del u)/(del y) .

If u=ax-by , then ((del u)/(del y))=

If u = log ((x ^ (2) + y ^ (2)) / (x + y)), prove that x (u) / (x) + y (u) / (y) = 1

If x^(x)y^(y)z^(z)=c. Then show that x=y=z(del^(2)z)/(del x backslash del y)=-(x log ex)^(-1)