If `u=(x-y)(y-z)(z-x)` show that `(delu)/(delx)+(delu)/(dely)+(delu)/(delz)=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 = (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 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)]

For conservative force field, vec(F)=-(delU)/(delx)hat(i)-(delU)/(dy)hat(j)-(delU)/(delz)hat(k) where Frarr Maginitude of Force. Urarr Potential energy and (delU)/(delx)= Differentiation of U w.r.t. x keeping y and z constant and so on. Choose incorrect matching :-

If x+y+z=0, then (x+y)(y+z)(z+x) is equal :

Simplify ((x-y)/(z)+(y-z)/(x)+(z-x)/(y))((z)/(x-y)+(x)/(y-z)+(y)/(z-x)) if x+y+z=0

If quad x+y+z=0 show that x^(3)+y^(3)+z^(3)=3xyz

If (y+z-x)/(log x)=y(z+x-y)/(log y)=z(x+y-z)/(log z) Prove that x^(y)y^(x)=z^(y)y^(z)=x^(z)z^(x)

From the equation ((delU)/(delV))_(T)=T((delP)/(delT))_(V)-P . Prove that for ideal gas ((delU)/(delV))_(T)=0.

(If(y+z-x))/((x(y+z-x))/(log y))=(y(z+x-y))/(log y)(z(x+y-z))/(log z), prove that x^(y)y^(x)=z^(x)y^(z)=x^(z)z^(x)