fluid dynamics - Why does the Vlasov equation not consider higher order time derivatives?

The Vlasov equation is given by: $$ \frac {df}{dt} = \frac {\partial f}{\partial t} + \vec{v} \cdot \frac {\partial f} {\partial \vec{x}} + \vec{a} \cdot \frac {\partial f} {\partial \vec{v}} $$

But why are higher order time-derivatives such as $ \frac {\partial \vec{a}} {\partial t} $ or $\frac {\partial f} {\partial \vec{a}}$ not included? Are they simply considered small or are they absolutely zero for some reason?