# Derivative

In English, **derivative** primarily refers to anything derived from a source - not primitive or original.

## Adjective

**derivative**

- Imitative of the work of someone else
- (
*copyright law*) Referring to a work, such as a translation or adaptation, based on another work that may be subject to copyright restrictions - Having a value that depends on an underlying asset of variable value
- Lacking originality

## Noun

**derivative** (*plural:* **derivatives**)

- Something derived.
- A word that derives from another one.
- A financial instrument whose value depends on the valuation of an underlying asset; such as a warrant, an option etc.
- A chemical derived from another.
- The derived function of a function.
*The derivative of f(x) = x^2 is f'(x) = 2x*

- The value of this function for a given value of its independent variable.
*The derivative of f(x) = x^2 at x = 3 is f'(3) = 2*3 = 6.*

## Synonyms

- (
*in analysis: function*): derived function - spinoff

## Antonyms

In copyright law, a **derivative work** is an artistic creation that includes major, basic copyrighted aspects of an original, previously created first work.

## United States law

In the United States, "derivative work" is defined in A “derivative work” is a work based upon one or more preexisting works, such as a translation, musical arrangement, dramatization, fictionalization, motion picture version, sound recording, art reproduction, abridgment, condensation, or any other form in which a work may be recast, transformed, or adapted. A work consisting of editorial revisions, annotations, elaborations, or other modifications which, as a whole, represent an original work of authorship, is a “derivative work”.

US Copyright Office Circular 14: Derivative Works notes that: A typical example of a derivative work received for registration in the Copyright Office is one that is primarily a new work but incorporates some previously published material. This previously published material makes the work a derivative work under the copyright law.

To be copyrightable, a derivative work must be different enough from the original to be regarded as a "new work" or must contain a substantial amount of new material. Making minor changes or additions of little substance to a preexisting work will not qualify the work as a new version for copyright purposes. The new material must be original and copyrightable in itself. Titles, short phrases, and format, for example, are not copyrightable.

WHO MAY PREPARE A DERIVATIVE WORK? Only the owner of copyright in a work has the right to prepare, or to authorize someone else to create, a new version of that work. The owner is generally the author or someone who has obtained rights from the author.

From another informative Artslaw Org website: The copyright provides the owner with a number of exclusive rights, including the right to make new versions of the original work, called derivative works. This concept also protects an artist from having his/her original work reproduced in a different media by another artist, without the consent of the first artist[1].

Stanford Law School Center Chilling Effects discusses 'Derivative Works'. If you are an author or an artist and you want to use all or part of someone else's creation in your work, you may run into problems with claims that your art is a derivative work[2].

On its FAQ page: Question: Can I take a character from a movie, like Chewbacca from Star Wars, and use it in a play with a very different plot and otherwise different characters? Answer: Probably not. The people who hold copyright in Star Wars own the characters as well as the plot, the filmed images, etc. Placing a distinctive fictional character in a different context or medium is still copying that character, and therefore infringement[3].

From Hudis Sullivan Copyright Article on 'derivative work': Although a derivative work author usually has been authorized, through license, to incorporate the previous work into his derivation, he does not gain thereby a copyright in any preexisting material.

Other courts, including the Eleventh Circuit Court of Appeals, take the view that an owner of a copyright registration for an original work should be permitted to sue for infringement of his derivative work without a separate registration. These courts proceed on the theory that (1) the original work author has the exclusive right to sue for infringement of his work; (2) a derivative work, by definition, includes the work that would be infringing without the consent of the original rights holder; and therefore (3) the original author's ability to sue on the original work carries over to any derivative work[4].

## Examples

Since many films are based on novels or scripts they are classed as derivative works. In cases where the film's copyright has lapsed but the original work is still covered, the film cannot be freely distributed without the permission of the original author on whose work the film was based.Cite error: Closing `</ref>`

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## Derivative work of software

The definition of derivative works of software is not entirely clear[5]

This is a particular problem for software that utilizes licenses such as the GPL because these licenses put special restrictions on such derivations (for instance the so-called viral clause of strong copyleft licenses asks for the new work to not further restrict the freedoms granted sofar).

Because the legal situation is not entirely certain, the following should thus only be taken as rules of thumb:

- If the original software is modified to create the new program, a derived work is created.
- If the original software was designed to accept plug-ins or drivers using a defined mechanism, such a driver or plug-in does not form a derived work.
- In the same sense linking to a library in the way it was designed to be interfaced with, does not constitute deriving a work.
*But See*LGPL.

A more detailed account on the issue can be found at Derivative Works by Lawrence Rosen.

## See also

## External links

- US Copyright Act (Hosted by the Copyright Office)
- US Copyright 'Derivative Works' (Hosted by the Copyright Office)
- Frequently Asked Questions (and Answers) about Derivative Works
- Article "Geek Law: Derivative Works" by Lawrence Rosen
- Article "DERIVATIVE WORK RIGHTS" by David M. Spatt
- Article "L.H.O.O.Q.--Internet-Related Derivative Works" by Richard H. Stern
- Article "Derivative Works" by Sarah Ovenall

In calculus, a branch of mathematics, the derivative is a measurement of how a function changes when the values of its inputs change. The derivative of a function at a chosen input value describes the best linear approximation of the function near that input value. For a real-valued function of a single real variable, the derivative at a point equals the slope of the tangent line to the graph of the function at that point. In higher dimensions, the derivative of a function at a point is a linear transformation called the linearization.[1]

The process of finding a derivative is called differentiation. The fundamental theorem of calculus states that differentiation is the reverse process to integration.