Where Does the Entropy Formula Come From in Thermodynamics?

[Master J]

Hey guys.

Right, I have been studying the Maxwell thermodynaic relations. But I have come across entropy as

dS = (bS/bT)_P(dT) + (bS/bP)_T(dP)

where b is the partial differential symbol.

I don't understand where this comes from, which suggests S(T,P). I can't find a derivation of this.

Could you help?

 

[nasu]

It's nothing really to derive. Physically, I mean.
For any function of two variables, the general formula for differentiation looks like this.
I mean, for f(x,y)
df=(bf/bx)dx+(bf/by)dy.

As for why S(p,T), you can use any two independent variables as "dependent variables".