Derive the following expression for the derivitive of Z with respect to pressure at constant tempreture and composition from the Peng$-$Robinson equation of state. Problem $5.(2$ points$)$ Derive the following expression for the derivative of $Z$

with respect to pressure at constant temperature and composition from the Peng$-$

Robinson equation of state $($PR$-$EOS$)$:

$(\frac{\text{d}\text{e}\text{l}\text{Z}}{\text{d}\text{e}\text{l}\text{p}}{)}_{T,N}=\frac{a}{R^2{T}^2}(\frac{B-Z}{3Z^2-2(1-B)Z+(A-3B^2-2B)})$

$+\frac{b}{RT}(\frac{-Z^2+2(3B+1)Z+(A-2B-3B^2)}{3Z^2-2(1-B)Z+(A-3B^2-2B)})$