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

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle dG=\left(\frac{\partial G}{\partial T}\right)_p dT + \left(\frac{\partial G}{\partial p}\right)_T dp}