Making use of the fact that the entropy \(S(N, V, E)\) of a thermodynamic system is an extensive quantity, show that

\[
N\left(\frac{\partial S}{\partial N}ight)_{V, E}+V\left(\frac{\partial S}{\partial V}ight)_{N, E}+E\left(\frac{\partial S}{\partial E}ight)_{N, V}=S
\]

Note that this result implies that \((-N \mu+P V+E) / T=S\), that is, \(N \mu=E+P V-T S\).