Why does $d(p^{1-\gamma}T^\gamma$) give $\frac{dp}{p} = \frac{\gamma}{\gamma - 1} \frac{dT}{T}$? If $(p^{1-\gamma}T^\gamma) = \text{constant}$?
where $p$ is pressure, $T$ is temperature and $\gamma = C_p/C_V$ is the ratio of heat capacities. I've seen examples of this kind of treatment where $d(pV) = p\,dV+V\,dp$, but I'm not sure enough of how it works to reproduce that on the expression above.