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 $\nabla f$ or $\operatorname {grad} f$.

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