Definition:Directional Derivative

Definition
Let:


 * $f: \R^n \to \R, \mathbf x \mapsto \map f {\mathbf x}$

be a real-valued function such that the gradient $\nabla \map f {\mathbf x}$ exists.

Let $\mathbf u$ be a unit vector in $\R^n$.

The directional derivative of $f$ in the direction of $\mathbf u$ is defined as:


 * $\dfrac \partial {\partial \mathbf u} \map f {\mathbf x} = \nabla \map f {\mathbf x} \cdot \mathbf u$

where $\cdot$ denotes the dot product.

Also see

 * Definition:Geometrical Representation of Gradient Operator