The
derivative
In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is t ...
of a function is the rate of change of the function's output relative to its input value.
Derivative may also refer to:
In mathematics and economics
*
Brzozowski derivative in the theory of formal languages
*
Covariant derivative
In mathematics and physics, covariance is a measure of how much two variables change together, and may refer to:
Statistics
* Covariance matrix, a matrix of covariances between a number of variables
* Covariance or cross-covariance between ...
, a way of specifying a derivative along
tangent vector
In mathematics, a tangent vector is a vector that is tangent to a curve or surface at a given point. Tangent vectors are described in the differential geometry of curves in the context of curves in R''n''. More generally, tangent vectors are ...
s of a
manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a N ...
with a
connection.
*
Exterior derivative, an extension of the concept of the
differential of a function to
differential forms of higher degree.
*
Formal derivative
In mathematics, the formal derivative is an operation on elements of a polynomial ring or a ring of formal power series that mimics the form of the derivative from calculus. Though they appear similar, the algebraic advantage of a formal deriv ...
, an operation on elements of a polynomial ring which mimics the form of the derivative from calculus
*
Fréchet derivative, a derivative defined on
normed spaces.
*
Gateaux derivative, a generalization of the concept of
directional derivative
In multivariable calculus, the directional derivative measures the rate at which a function changes in a particular direction at a given point.
The directional derivative of a multivariable differentiable (scalar) function along a given vect ...
in
differential calculus
In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus—the study of the area beneath a curve. ...
.
*
Lie derivative, the change of a
tensor field (including scalar functions,
vector fields and
one-forms), along the
flow defined by another vector field.
*
Radon–Nikodym derivative in measure theory
*
Derivative (set theory), a concept applicable to normal functions
*
Derivative (graph theory), an alternative term for a line graph
*
Derivative (finance)
In finance, a derivative is a contract between a buyer and a seller. The derivative can take various forms, depending on the transaction, but every derivative has the following four elements:
# an item (the "underlier") that can or must be bou ...
, a contract whose value is derived from that of other quantities
*
Derivative suit or derivative action, a type of lawsuit filed by shareholders of a corporation
In science and engineering
*
Derivative (chemistry), a type of compound which is a product of the process of derivatization
*
Derivative (linguistics)
Morphological derivation, in linguistics, is the process of forming a new word from an existing word, often by adding a prefix or suffix, such as For example, ''unhappy'' and ''happiness'' derive from the root word ''happy.''
It is differentiat ...
, the process of forming a new word on the basis of an existing word, e.g. happiness and unhappy from happy
*
Aeroderivative gas turbine, a mechanical drive gas turbine derived from an aero engine gas turbine
Other uses
*
Derivative work
In copyright law, a derivative work is an expressive creation that includes major copyrightable elements of a first, previously created original work (the underlying work). The derivative work becomes a second, separate work independent from ...
, in copyright law, a modification of an original work
**
Fork (software development)
In software development, a fork is a codebase that is created by duplicating an existing codebase and, generally, is subsequently modified independently of the original. Software built from a fork initially has identical behavior as software ...
*
''Derivative'' (film), a 2005 Turkish film
*Derivative Inc., a spin-off of Side Effects Software, creators of the software
Houdini
*Derivative, used to describe a word formed from another word
See also
*
Derive (disambiguation), for meanings of "derive" and "derived"
*
Derivation (disambiguation)
Derivation may refer to:
Language
* Morphological derivation, a word-formation process
* Parse tree or concrete syntax tree, representing a string's syntax in formal grammars
Law
* Derivative work, in copyright law
* Derivation proceeding, a pro ...
*
Imitation
*
Interpretation (disambiguation)
*
Mimicry
In evolutionary biology, mimicry is an evolved resemblance between an organism and another object, often an organism of another species. Mimicry may evolve between different species, or between individuals of the same species. In the simples ...
*
{{disambiguation