In mathematics, the gradient is a generalization of the usual concept of derivative to the functions of several variables. If is a differentiable function of several variables, also called "scalar field", its gradient is the vector of the n partial derivatives of f. It is thus a vector-valued function also called vector field.

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#### Noun

1. A slope or incline.
2. A rate of inclination or declination of a slope.
3. Of a function y = f(x) or the graph of such a function, the rate of change of y with respect to x, that is, the amount by which y changes for a certain (often unit) change in x.
4. The rate at which a physical quantity increases or decreases relative to change in a given variable, especially distance.
5. A vector operator that maps each value of a scalar field to a vector equal to the greatest rate of change of the scalar. Notation for a scalar field φ: [itex]\nabla[/itex]φ