.If `(x^(2))/(a^(2)+b^(2))+(y^(2))/(b^(2)+a^(2))+(z^(2))/(c^(2)+b^(2))=u`,find `((del u)/(del x))+((del u)/(del y))+((del u)/(del z))=?`

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

u=(x^(2)-y^(2))/(x^(2)+y^(2)) find d(u)/(dx)?

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

(x-y)^(2) (dy)/(dx) =a^(2), x -y =u

If x = r cos theta and y = r sin theta, prove that (del ^ (2) r) / (del x ^ (2)) + (del ^ (2) r) / (del y ^ (2)) = (1) / (r) [((del r) / (del x)) ^ (2) + ((del r) / (del y)) ^ (2)]

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 (a^(2)+b^(2)+c^(2))(x^(2)+y^(2)+z^(2))=(ax+by+cz)^(2), then show that x:a=y:b=z:c