Which one of the following is the correct thermodynamic equation of state?

1
\(dG = \left(\frac{\partial G}{\partial P}\right)_T\) \(dP + \left(\frac{\partial G}{\partial P}\right)_P \ dT\)
2
\(\left(\frac{\partial U}{\partial V}\right)_T=P+T\left(\frac{\partial P}{\partial T}\right)_V\)
3
\(dU=\left(\frac{\partial U}{\partial V}\right)_S \ dV + \left(\frac{\partial U}{\partial S}\right)_V \ dS\)
4
\(\left(\frac{\partial H}{\partial P}\right)_T= \ V-T \left(\frac{\partial V}{\partial T}\right)_{p,n}\)
5
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