Definition
Given a set {% U \subset \mathbb{R}^n %} and a function {% f:U \rightarrow \mathbb{R} %}. For a curve {% \gamma:(- \epsilon,\epsilon) \rightarrow U %} with {% \gamma(0) = p \in U %} and {% \gamma'(0) = \vec{v} %}. The directional derivative of {% f %} in the direction {% \vec{v} %} is defined to be
{% \lim_{t \to 0} \frac{f(\gamma(t)) - f(p)}{t} %}
(see Doria pg. 2)