# Oh Yeah

Given a vector function, I show that $\vec{F}(x,y,z,t)$, I show that $d\vec{F} = (d\vec{r} \cdot \nabla) \vec{F} + \frac{\partial \vec{F}}{\partial t}$  by writing $d\vec{F}$ in terms of independent variations in the $x, y, z$ and $t$ direction. I write $d\vec{F}$ as a sum of four increments, one purely in the $x$ direction, the $y$ direction, the $z$ direction and the $t$ direction as follows: