Establish thermodynamically the formulae

\[
V\left(\frac{\partial P}{\partial T}ight)_{\mu}=S \quad \text { and } \quad V\left(\frac{\partial P}{\partial \mu}ight)_{T}=N
\]

Express the pressure \(P\) of an ideal classical gas in terms of the variables \(\mu\) and \(T\), and verify the above formulae.