I think that there is an ambiguity for defining the time derivative of a superfunction on the phase space of pseudo-classical mechanics of Grassmann numbers.
Let $\xi$ be a Grassmann odd number. Its canonical conjugate variable is $p$. Let $f(p,\xi)$ be a superfunction defined on the phase space $(p,\xi)$ of "classical fermions". The time derivative can be defined in two ways:
$\dot{f}=\dot{\xi}\frac{\overrightarrow{\partial}}{\partial\xi}f+\dot{p}\frac{\overrightarrow{\partial}}{\partial p}f$,
$\dot{f}=f\frac{\overleftarrow{\partial}}{\partial\xi}\dot{\xi}+f\frac{\overleftarrow{\partial}}{\partial p}\dot{p}$.
Which definition should I use?