If `x^xy^yz^z = c.` Then show that at `x = y = z;` `(del^2z)/(delx\ dely) = -(x log ex)^(-1)`

If x^(x)y^(y)z^(z)=c. Then show that x=y=z(del^(2)z)/(del x backslash del y)=-(x log ex)^(-1)

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 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 x,y,z are in HP, then show that log(x+z)+log(x+z-2y)=2 log (x-z)

If xy + yz + zx = 1 , show that x/(1-x^(2)) +y/(1-y^(2)) + z/(1-z^(2))= (4xyz)/((1-x^(2))(1-y^(2)) (1-z^(2)))

If x + y + z = 0 , then the value of (x^2)/(yz) + (y^2)/(zx) + (z^2)/(xy) is:

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 xy + yz + zx = 1 , show that x/(1-x^(2)) +y/(1-y^(2)) + z/(1-z^(2))= 4xyz/((1-x^(2))(1-y^(2)) (1-z^(2)))