Gradient

In mathematics, the gradient of a real-valued differentiable function <math>f(x_1,...,x_n)</math> at a point <math>p</math> is a vector in <math>R^n</math> which points in the direction in which <math>f</math> increases most rapidly. The magnitude of the gradient at <math>p</math> is equal to the maximum directional derivative of <math>f</math> at <math>p</math>.

More precisely, the gradient of <math>f</math> is the vector-field:

<math> (\frac{\partial f}{\partial x_1},...,\frac{\partial f}{\partial x_n}) </math>