For one mole the ideal gas law is pV=RT , write down the exact differential dV.

Question

Would I be right to differentiate with respect to T and p separately?...
V = RT/p
dV = R/p - (RT)/(p^2)

Answer 1

I think they mean
dV = (R/p) dT - (RT)/(p^2) dp

This satisfies the requirement that the partial derivative of (R/p) with respect to p equals the partial derivative of (RT)/(p^2) with respect to T.

See
http://mathworld.wolfram.com/ExactDifferential.html
for more about exact differentials