# Definify.com

## Gra′di-ent

,
[L.
,
p. pr.
of
to step, to go. See
.]
1.
Moving by steps; walking;
as,
automata
.
Wilkins.
2.
Rising or descending by regular degrees of inclination;
as, the
line of a railroad
.
3.
Adapted for walking, as the feet of certain birds.

## Gra′di-ent

,
Noun.
1.
The rate of regular or graded ascent or descent in a road; grade.
2.
A part of a road which slopes upward or downward; a portion of a way not level; a grade.

## GRA'DIENT

,
[L. gradiens, gradior.] Moving by steps; walking; as gradient automata.

## English

### Noun

1. A slope or incline.
2. A rate of inclination or declination of a slope.
3. (calculus) 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
equivalently, the inclination to the X axis of the tangent to the curve of the graph.
4. (sciences) The rate at which a physical quantity increases or decreases relative to change in a given variable, especially distance.
5. (analysis) A differential operator that maps each point of a scalar field to a vector pointed in the direction of the greatest rate of change of the scalar. Notation for a scalar field φ: φ

#### Translations

1. Moving by steps; walking.
(Can we find and add a quotation of Wilkins to this entry?)
2. Rising or descending by regular degrees of inclination.
3. Adapted for walking, as the feet of certain birds.