How to find an equation relating dp and the differentials dv and dt from the ideal gas law pV=RT?

pV = n * R * T

That's the Ideal Gas Law

Use the product rule

P * V = n * R * T

P * dV/dt + V * dP/dt = n * R * dT/dt

n and R are kept as constant, so we can represent them as k

P * dV/dt + V * dP/dt = k * dT/dt

V * dP/dt = k * dT/dt - P * dV/dt

dP/dt = (k * dT/dt - P * dV/dt) / V

pV=RT......(i)

Differentiatiing partially gives

pdV+dpV=RdT....(ii)

Dividing (ii) by (i) gives

(pdV+dpV)/pV=RdT/RT

→dv/V+dp/p=dT/T