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 ${\displaystyle \nabla f}$ 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.

## References

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". mathworld.wolfram.com. Retrieved 2020-09-16.