# Jacobian vs Gradient - What's the difference?

## 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

(-)
• 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.

## English

### Noun

• 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 )