Gradient

For other uses, see Gradient (disambiguation).

The values of the function are shown in black and white. The darker areas have higher values. The blue arrows show the gradient.

In vector calculus, the gradient of a multivariate function measures how steep a curve is. On a graph of the function, it is the slope of the tangent of that curve. More generally, it is a vector that points in the direction in which the function grows the fastest. Its coordinates are partial derivatives of that function. The gradient of a function f is often written as [math]\displaystyle{ \nabla f }[/math] or [math]\displaystyle{ \operatorname{grad} f }[/math].

Gradient Media

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  Gradient of the 2D function f(x, y) = xe−(x2 + y2) is plotted as arrows over the pseudocolor plot of the function.

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  The gradient of the function f(x,y) = −(cos2x + cos2y)2 depicted as a projected vector field on the bottom plane.

Related pages

• Laplace operator