Adiabatic Expansion - proof of PV^(gamma) = constant

CAF123

Hi,

I was looking at the proof for the derivation of the condition satisfied by adiabatic processes. (The proof can be found in many introductory physics textbooks, I am using Principles of Physics HRW 9th ed.) At some point , they say 'For an ideal gas PV=nRT and if P,V T are allowed to take on small variations we have that PdV + VdP = nRdT'. Where does the part in bold come from, specifically the PdV +VdP?

Sorry if I have overlooked something obvious.

vin300

The derivative of product of variables. d(PV)=VdP +PdV