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Line 1: − :''This article deals with the advanced concept of gradient in a vector field'' − :''For the simplied gradient used in early high school see: [[Gradient (two points)]]''
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{{math-a}}
{{math-a}}
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 at <math>p</math>. The magnitude of the gradient at <math>p</math> is equal to the maximum directional derivative of <math>f</math> at <math>p</math>.
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 at <math>p</math>. The magnitude of the gradient at <math>p</math> is equal to the maximum directional derivative of <math>f</math> at <math>p</math>.