Section 14.3 Partial Derivatives

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. Show that
\[\frac{\partial P}{\partial V} \frac{\partial V}{\partial T} \frac{\partial T}{\partial P} = -1\]