Gradient

analysis

Definition

Gradient

Let $D\subseteq {\mathbb{R}}^n$ an open set and $f:D\to \mathbb{R}$ a totally differentiable function, then the vector

$$\mathrm{grad}f=\nabla f=\left[\begin{array}{c}\frac{\partial }{\partial x_1}f\\ \frac{\partial }{\partial x_2}f\\ ⋮\\ \frac{\partial }{\partial x_n}f\end{array}\right]$$

is called the gradient of $f$.