Partial Derivatives and Constant Variables in Thermodynamics

[Jalo]

Homework Statement

Consider the following equality:

($\frac{∂S}{∂V}$)_T = ($\frac{∂P}{∂T}$)_V

If I rearrange the equality so that I write:

($\frac{∂S}{∂P}$)_? = ($\frac{∂V}{∂T}$)_?

What variables will be constant in each side?
I'm having some trouble in a few thermodynamics problems because of this...

Homework Equations

The Attempt at a Solution

I don't know how to do this. Normally I just ignore and assume that every variable except the variable of differentiation is a constant.
If anyone could confirm or correct me I'd be thankful.

Thanks.

 

[Isaac0427]

I think (T/V)(∂s/∂p)=(∂V/∂T). Is this correct?