If `u=f(y-z,z-x,x-y)`, Prove that: `(delu)/(delx)+(delu)/(dely)+(delu)/(delz)=0`

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^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 |(a,y,z),(x,b,z),(x,y,c)|=0 , then prove that (a)/(a-x)+(b)/(b-y)+(c)/(c-z)=2

If 2^(x)=3^(y)=6^(-z) prove that (1)/(x)+(1)/(y)+(1)/(z)=0

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

If x,y,z gt 0 then prove that (x+y+z)(1/x+1/y+1/z) geq 9

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