Translations:The directional derivative/6/en

In general, we want to know the slope in some arbitrary direction. Recall that a unit vector is a vector with length, or magnitude, of one. We can convert any vector into a unit vector in the same direction by dividing the vector by its magnitude. Hence, the unit vector for direction angle $\gamma$ (as measured from the horizontal) can be represented by $\mathbf {w=} \left({\rm {\ cos\ }}\gamma {\rm {,\ sin\ }}\gamma \right)$. If we let $\sigma$ represent distance in the direction of the vector w, then