Gradient

A Vector Space representing the rate of change for a function with multiple inputs and a single output. Will always point to the direction of maximum increase.

Definition

The gradient of $f:{\mathbb{R}}^n\to \mathbb{R}$ is defined as: $\nabla f=Df=[\frac{\partial f}{\partial x},\dots ,\frac{\partial f}{\partial x_n}]$