In calculus terms the difference between jacobian and gradient
is that
jacobian is the determinant of such a matrix while
gradient is 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.
jacobian English
Adjective
( )
 The Jacobian matrix has partial derivatives as its entries.
Noun
( en noun)
(calculus) A Jacobian matrix or its associated operator.
(calculus) The determinant of such a matrix.

gradient English
Noun
( en noun)
( slope)
( wikipedia gradient)
A slope or incline.
A rate of inclination or declination of a slope.
(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.
(science) The rate at which a physical quantity increases or decreases relative to change in a given variable, especially distance.
(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
Synonyms
* (slope) hill, incline, ramp, slope
* (in calculus) slope (of a line )
Derived terms
* gradient wind
* ruling gradient
* supergradient
* temperature gradient
Adjective
( )
Moving by steps; walking.
 gradient automata
 (Wilkins)
Rising or descending by regular degrees of inclination.
 the gradient line of a railroad
Adapted for walking, as the feet of certain birds.
Anagrams
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*
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