(HARD) I'd be surprised if anyone can do this one...?

This is an advanced university mathematics problem involving thermodynamic equalities (but mostly about the math). Attempt at your own risk :)

If F(P,V,T) = 0 then prove the following:

Note: All 'd's are meant to be dy's (as in, partial derivatives).

The "_'letter' " are the subscripts for that partial derivative, that is, the variable which is to be held constant.

The spaces are just multiplications. I spaced them out to make it easier to read.

So here they are, prove these two relations.

dP/dT _V dP/dV _P = -dP/dV _T

and also prove

dP/dT_V dT/dV_P dV/dP_T = -1

Note: These results are useful in thermodynamics where P,V,T correspond to pressure, volume and temperature of a physical system.

That is all the information given in the problem.

Kudos to anyone who can figure it out. I've been staring for a while with no success... Granted I've been doing math all day, so maybe I'm just not seeing it.