How can I get this equation?

I need to get dp/p = -a*dT + k*dP.
I have k = -1/V * (δV/δP)
a = 1/V * (δV/δt), a = -1/p * (δp/δT) and p = N/V
Note that p does not equal P.
I'm still working on this, but I'm not making much progress.

Hey Shanter.

For dV/dP, use the fact that V=N/p and differentiate (you will have to use the quotient rule if N is not independent from P) which will give something in terms of p.

so if N is not independent than do I get (p(dN/dp) - N)/p^2? I don't see how that helps

The point is to get rid of the V's and the other terms not in the expression so you can collect and simplify the terms.

Also I think you can assume N to be indepedent which simplifies things greatly and my reasoning is that if it wasn't it would be labelled N(p) or the expression would be simplified to some grand function of p.

Ok I think I got it now, but I'm not sure about some of the math. I get dp/p = -dV/V from dV/dp of V=N/p. Using a = 1/V * (δV/δt) i get δV = V*a*dT and using k = -1/V * (δV/δP) I get δV = -V*dP*k.
So can does dV = δV+δV here? I get the right answer, but that doesn't feel right to me.