Gibbs energy function

Definition:

$\left.G\right.=A+pV$

$\left.G\right.=U-TS+pV$

Taking the total derivative

$\left.dG\right.=dU-TdS-SdT+pdV+Vdp$

From the Second law of thermodynamics one obtains

$\left.dG\right.=TdS-pdV-TdS-SdT+pdV+Vdp$

thus one arrives at

$\left.dG\right.=-SdT+Vdp$

For G(T,p) we have the following total differential

$dG=\left({\frac {\partial G}{\partial T}}\right)_{p}dT+\left({\frac {\partial G}{\partial p}}\right)_{T}dp$

Good for $NpT$