I know if $\vec u$ is a unit vector, then $\triangledown(x,y) \bullet \vec u$ is the directional derivative, or $D_{u}(a,b)$
However, if $u$ is a vector, when $f_{\vec u}(a,b)$ is a real, what does it mean? $u_xf_x(a,b)+u_yf_y(a,b)$?
When it is a vector, what does it mean? $\langle u_xf_x(a,b),u_yf_y(a,b) \rangle$?