Gradient

It points in the direction of the greatest rate of increase of the function, and its magnitude gives the rate of increase in that direction.

The gradient is a vector composed of the partial derivatives of the function with respect to each of its variables, where $f:{\mathbb{R}}^n\to \mathbb{R}$.

$$\nabla f(x)=[\frac{\partial f}{\partial x}{]}^T=\left[\begin{array}{ccc}\frac{\partial f}{\partial x_1}& \dots & \frac{\partial f}{\partial x_n}\end{array}\right]$$

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