I am reading Sakurai's Modern quantum mechanics and at some point it's trying to draw a parallel between classical and quantum mechanics.
It says
An infinitesimal translation in classical mechanics can be regarded as a canonical transformation, $$ \mathbf{x}_{\mathrm{new}} \equiv \mathbf{X} = \mathbf{x} + d\mathbf{x}, \quad \mathbf{p}_{\mathrm{new}} \equiv \mathbf{P} = \mathbf{p}, \tag{1.6.28} $$ obtainable from the generating function $$ F_2(\mathbf{x}, \mathbf{P}) = \mathbf{x}\cdot \mathbf{P} + \mathbf{p}\cdot d\mathbf{x}. \tag{1.6.29} $$
From the wikipedia page it seems that a generating function is something that one can differentiate to obtain the equation of motion of the system.
I mean I assume I need to differentiate $F$ with respect to $\mathbf{X}$ and $\mathbf{P}$? What equation of motion am I supposed to get from here?