Finding Entropy with three natural variables

[Katie1990]

Homework Statement

Given

G =U −TS+PV −BaM

show that

S(T,Ba,P) = -(dG/dT)Ba,P

Homework Equations

The Attempt at a Solution

I know how to proceed if there are two variables and attemped to use this giving

dG = dU - TdS - SdT +PdV +VdP - BadM -MdBa

Using central equation

dG = = SdT +VdP -BadM - MdBa

I am unable to proceed from here

 

[Mapes]

If you are going to include magnetic energy in the problem, your $dU$ equation will need to include a $B\,dM$ term. Does this help you finish?