From my notes:
Given a vector $\vec{v}=(v_1,v_2)$ on $\mathbb{R}^2$, the directional derivative $\nabla_\vec{v}f$ of the function $f=f(x,y)$ in the direction of $f$ is defined by:
$$\nabla_\vec{v}f=\vec{v}\cdot\nabla f=v_1f_x+v_2f_y$$
where $|\cdot|$ denotes the inner product. This direction gives the change of $f$ in the direction of $\vec{v}$.
Now, I don't fully understand the last sentence. I don't know what "this direction" is referring to, and am getting confused. Is it referring to the directional derivative - in which case, the sentence says the following?
The directional derivative gives the change of function f in the direction of $\vec{v}$?