Please provide all the steps and solution

The Thomas-Fermi von-Weizsicker formula for the energy of an electron gas of density p(X), over a region of space ( is given as the functional: 1Vp(X).Vp(X Elp] = [ (G + 5 4 p (g} av Here, C is a constant, (X) (not dependent on the density p(X)) is a specified potential field that is typically of electrostatic origin and the electron density integrates to the number of electrons enclosed within the volume (), i.e, fn p(x) AV = N,jectrons- Based on this information, derive a formula for the chemical potential for such a system. (15 points) [Hint: Use Lagrange multipliers to enforce the constraint of fixed particle number]