Gradient

For other uses, see Gradient (disambiguation).

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 ${\displaystyle \nabla f}$ or ${\displaystyle \operatorname {grad} f}$.^[1][2][3]

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

Related pages

• Laplace operator