The gas law for a fixed mass $m$ of an ideal gas at absolute temperature $T$, pressure $P$, and volume $V$ is $PV = mRT$, where $R$ is the gas constant. Find the partial derivatives
$\displaystyle \frac{\partial P}{\partial V} =$
$\displaystyle \frac{\partial V}{\partial T} =$
$\displaystyle \frac{\partial T}{\partial P} =$
$\displaystyle \frac{\partial P}{\partial V} \frac{\partial V}{\partial T}\frac{\partial T}{\partial P} =$ (an integer)