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 theoretical computer science, in particular in formal language theory, the Brzozowski derivative u^S of a set (mathematics), set S of word (formal languages), strings and a string u is the set of all strings obtainable from a string in S by cu ...

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 Connection may refer to: Mathematics *Connection (algebraic framework) *Connection (mathematics), a way of specifying a derivative of a geometrical object along a vector field on a manifold * Connection (affine bundle) *Connection (composite bun ...

. *

Exterior derivative On a differentiable manifold, the exterior derivative extends the concept of the differential of a function to differential forms of higher degree. The exterior derivative was first described in its current form by Élie Cartan in 1899. The re ...

, an extension of the concept of the differential of a function to

differential form In mathematics, differential forms provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds. The modern notion of differential forms was pioneered by Élie Cartan. It has many applications ...

s 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 In mathematics, the Fréchet derivative is a derivative defined on normed spaces. Named after Maurice Fréchet, it is commonly used to generalize the derivative of a real-valued function of a single real variable to the case of a vector-valued f ...

, a derivative defined on

normed space The Ateliers et Chantiers de France (ACF, Workshops and Shipyards of France) was a major shipyard that was established in Dunkirk, France, in 1898. The shipyard boomed in the period before World War I (1914–18), but struggled in the inter-war p ...

s. *

Gateaux derivative In mathematics, the Gateaux differential or Gateaux derivative is a generalization of the concept of directional derivative in differential calculus. Named after René Gateaux, it is defined for functions between locally convex topological vect ...

, 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 ...

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 In differential geometry, the Lie derivative ( ), named after Sophus Lie by Władysław Ślebodziński, evaluates the change of a tensor field (including scalar functions, vector fields and one-forms), along the flow defined by another vector fi ...

, the change of a

tensor field In mathematics and physics, a tensor field is a function assigning a tensor to each point of a region of a mathematical space (typically a Euclidean space or manifold) or of the physical space. Tensor fields are used in differential geometry, ...

(including scalar functions,

vector field In vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean space \mathbb^n. A vector field on a plane can be visualized as a collection of arrows with given magnitudes and dire ...

s and

one-form In differential geometry, a one-form (or covector field) on a differentiable manifold is a differential form of degree one, that is, a smooth section of the cotangent bundle. Equivalently, a one-form on a manifold M is a smooth mapping of the to ...

s), along the

flow Flow may refer to: Science and technology * Fluid flow, the motion of a gas or liquid * Flow (geomorphology), a type of mass wasting or slope movement in geomorphology * Flow (mathematics), a group action of the real numbers on a set * Flow (psyc ...

defined by another vector field. * Radon–Nikodym derivative in measure theory *

Derivative (set theory) In axiomatic set theory, a function is called normal (or a normal function) if it is continuous (with respect to the order topology) and strictly monotonically increasing. This is equivalent to the following two conditions: # For every limit o ...

, a concept applicable to normal functions *

Derivative (graph theory) In the mathematical discipline of graph theory, the line graph of an undirected graph is another graph that represents the adjacencies between edges of . is constructed in the following way: for each edge in , make a vertex in ; for every ...

, 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 A shareholder derivative suit is a lawsuit brought by a shareholder on behalf of a corporation against a third party. Often, the third party is an insider of the corporation, such as an executive officer or director. Shareholder derivative suits are ...

or derivative action, a type of lawsuit filed by shareholders of a corporation

In science and engineering

Derivative (chemistry) In chemistry, a derivative is a compound that is derived from a similar compound by a chemical reaction. In the past, derivative also meant a compound that ''can be imagined to'' arise from another compound, if one atom or group of atoms is rep ...

, 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 gas turbine or gas turbine engine is a type of continuous flow internal combustion engine. The main parts common to all gas turbine engines form the power-producing part (known as the gas generator or core) and are, in the direction of flow: ...

, 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 Erik Weisz (March 24, 1874 – October 31, 1926), known professionally as Harry Houdini ( ), was a Hungarian-American escapologist, illusionist, and stunt performer noted for his escape acts. Houdini first attracted notice in vaudeville in ...

*Derivative, used to describe a word formed from another word

In mathematics and economics

In science and engineering

Other uses

See also