Gradient

Gradient is about calculating the partial derivative of a function with several input variables. The gradient of a function $f\colon \mathbb {R} ^{n}\to \mathbb {R}$ is usually written as $\nabla f$. Gradient is a function $\nabla f\colon \mathbb {R} ^{n}\to \mathbb {R} ^{n}$. Therefore, it is actually a vector field. Its value at point $p=(x_{1},\ldots ,x_{n})$ is

$$\nabla f(p)={\begin{bmatrix}{\frac {\partial f}{\partial x_{1}}}(p)\\\vdots \\{\frac {\partial f}{\partial x_{n}}}(p)\end{bmatrix}}.$$