If `u=y/z+z/x` show that `x(delu)/(delx)+y(delu)/(dely)+z(delu)/(delz)=0`

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 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 :-

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

If x + y = 2z then (x)/(x-z) +(z)/(y-z) = ?

If x=y^z,y=z^x,z=x^y then

If x+y+z=,0, show that x,y,zx^(2),y^(2),z^(2)y+z,z+x,x+y]|=0

If x+y+z=0 , show that : cot(x+y-z) cot (z+x-y) +(cot(x+y-z) cot (y+z-x)+cot(y+z-x) cot (z+x-y)=1

If (log x)/(y-z)=(log y)/(z-x)=(log z)/(x-y), then prove that: x^(x)y^(y)z^(z)=1