The Maxwell relation derived from the differential expression for the Helmholtz free energy (dA) is

Answer: Option D

Helmholtz function :
$$\begin{array}{l}A=U-TS\\ \Rightarrow dA=-PdV-SdT\end{array}$$
So, we can derive the Maxwell function : $${\left(\frac{\partial P}{\partial T}\right)}_V={\left(\frac{\partial S}{\partial V}\right)}_T$$