If `u=(x^2+y^2+z^2)^(-1/2)`, show that `x(delu)/(delx)+y(delu)/(dely)+z(delu)/(delz)=-u`

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

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 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 2^(x)=3^(y)=12^(z) show that (1)/(z)=(1)/(y)+(2)/(x)

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

If u = x ^ (4), show that (y ^ (3) u) / (y x ^ (2)) = (^ (3) u) / (x and x)

If (x+iy)^(3)=u+iv, then show that (u)/(x)+(v)/(y)=4(x^(2)-y^(2))

If (x+iy)^(3)=u+iv then show that (u)/(x)+(v)/(y)=4(x^(2)-y^(2))

If z=x+iy and |z-1|+|z+1|=4 show that 3x^(2)+4y^(2)=12