If (f(S, T, P)=0), then by following the cyclic relation, prove that [ left(frac{partial S}{partial T} ight)_{P}left(frac{partial

If \(f(S, T, P)=0\), then by following the cyclic relation, prove that

\[ \left(\frac{\partial S}{\partial T}\right)_{P}\left(\frac{\partial T}{\partial P}\right)_{S}\left(\frac{\partial P}{\partial S}\right)_{T}=-1 \]

One variable is assumed to be dependent on the other two.