derivation of a PDE describing traffic flow

[Shaghayegh A]

In example 8 of chapter 2.1 where we derive a PDE describing traffic flow, how do we derive $ρ_t+vρ_x=0\;(6)$ from $p_t+q_x=0\;(3)\;?$

It seems that $q_x$ some how equals $vp_x=[c(\rho)+ c' (\rho)\rho] \;p_x=c(p) \frac{\partial p}{\partial x}+\frac{d c(p)}{p} p \frac{\partial p}{\partial x}$? Can someone please explain how we get equation (6)? Thanks

[Victor Ivrii]

You plug $q= q(\rho)$ into $\rho_t + q_x=0$