The Maxwell relation derived from the differential expression for the Helmholtz free energy (dA) is
(∂T/∂V)S = - (∂P/∂S)V
(∂S/∂P)T = - (∂V/∂T)P
(∂V/∂S)P = (∂T/∂P)S
(∂S/∂V)T = (∂P/∂T)V
(∂T/∂V)S = - (∂P/∂S)V
(∂S/∂P)T = - (∂V/∂T)P
(∂V/∂S)P = (∂T/∂P)S
(∂S/∂V)T = (∂P/∂T)V