For instance, the Maxwell equations for Thermodynamics:

    \begin{align} dU &= TdS - PdV &\Longrightarrow \left(\frac{\partial T}{\partial V}\right)_S = -\left(\frac{\partial P}{\partial S}\right)_V\\ dA &= -SdT - PdV &\Longrightarrow \left(\frac{\partial S}{\partial V}\right)_T =\left(\frac{\partial P}{\partial T}\right)_V\\ dH &= TdS +VdP &\Longrightarrow \left(\frac{\partial T}{\partial P}\right)_S = \left(\frac{\partial V}{\partial S}\right)_P\\ dG &= -SdT +VdP &\Longrightarrow -\left(\frac{\partial S}{\partial P}\right)_T = \left(\frac{\partial V}{\partial T}\right)_P\\ \end{align}

This leaves something to be desired....