multi-variable generalization of the derivative

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 or .[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.

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References change

  1. "List of Calculus and Analysis Symbols". Math Vault. 2020-05-11. Retrieved 2020-09-16.
  2. "The gradient vector | Multivariable calculus (article)". Khan Academy. Retrieved 2020-09-16.
  3. Weisstein, Eric W. "Gradient". Retrieved 2020-09-16.