Gibbs energy function

Definition:

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

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

Taking the total derivative

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

but from equation \ref{secondlaw} we obtain

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \left.dG\right.=TdS-pdV-TdS-SdT+pdV+Vdp}

thus one arrives at

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \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 $NpT$