Skip to content


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}}.