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Topic: Derivative

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  Derivative - Wikipedia, the free encyclopedia
If the second derivative is positive at a critical point, that point is a local minimum; if negative, it is a local maximum; if zero, it may or may not be a local minimum or local maximum.
The derivatives of sin(x), ln(x) and exp(x) can be found in table of derivatives, but the vast majority of mathematicians and maths students learn the derivatives of such common functions off by heart.
The common thread is that the derivative at a point serves as a linear approximation of the function at that point.
en.wikipedia.org /wiki/Derivative#Differentiation_and_differentiability   (2343 words)

 Derivative work - Wikipedia, the free encyclopedia
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.
If a derivative work is created with the permission of the original creator, the secondary creator maintains a copyright interest in only the aspects of the derivative work that are his or her original creations.
With certain software licenses such as the GPL the problem arises to define a derivative work of a software 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).
en.wikipedia.org /wiki/Derivative_work   (900 words)

 [No title]   (Site not responding. Last check: 2007-10-22)
Derivatives are defined by taking the limit of a secant slope, as its two points of intersection (with f(x)) converge; the secant approaches a tangent.
Mathematically, we define the derivative to be the limit of this ratio, as h tends to zero.
If the second derivative is positive at a stationary point, that point is a local minimum; if negative, it is a local maximum; if zero, it may or may not be a local minimum or local maximum.
www.wikiwhat.com /encyclopedia/d/de/derivative.html   (1461 words)

 PlanetMath: derivative
Qualitatively the derivative is a measure of the change of a function in a small region around a specified point.
Since the notion of a manifold was constructed specifically to generalize the notion of a derivative, this seems like the end of the road for this entry.
This is version 17 of derivative, born on 2002-05-31, modified 2005-11-04.
planetmath.org /encyclopedia/Derivative2.html#line   (780 words)

 The Derivative   (Site not responding. Last check: 2007-10-22)
The ordinary derivative of a function of one variable can be carried out because everything else in the function is a constant and does not affect the process of differentiation.
One example of the use of the derivative is in obtaining the velocity and acceleration from a position equation.
The derivative of a polynomial is the sum of the derivatives of its terms, and for a general term of a polynomial such as
hyperphysics.phy-astr.gsu.edu /hbase/deriv.html   (203 words)

 Derivative   (Site not responding. Last check: 2007-10-22)
In mathematics the derivative of a function is one of the two central of calculus.
The derivative of a function at a point is a measure of the rate which that function is changing as an argument undergoes change.
The common thread is the derivative at a point serves as linear approximation of the function at that Perhaps the most natural situation is that functions between differentiable manifolds ; the derivative at a certain point becomes a linear transformation between the corresponding tangent spaces and the derivative function becomes a between the tangent bundles.
www.freeglossary.com /Derivative   (2312 words)

 Derivative - Wikipedia, the free encyclopedia
The simplest notation for differentiation that is in current use is due to Joseph Louis Lagrange and uses the prime mark:
Euler's notation is useful for stating and solving linear differential equations.
Perhaps the most natural situation is that of functions between differentiable manifolds; the derivative at a certain point then becomes a linear transformation between the corresponding tangent spaces and the derivative function becomes a map between the tangent bundles.
en.wikipedia.org /wiki/Derivative   (2343 words)

 Derivative   (Site not responding. Last check: 2007-10-22)
Category:Calculus In mathematics, the derivative of a function is one of the two central concepts of calculus.
(The other one is the antiderivative, the inverse of the derivative.) The derivative of a function at a point measures the rate at which the function's value changes as the function's argument changes.
right Derivatives are defined by taking the limit of the slope of secant lines as they approach a tangent line.
derivative.kiwiki.homeip.net   (2300 words)

 Legal Definition of 'Derivative'
DERIVATIVE - Coming from another; taken from something preceding, secondary; as derivative title, which is that acquired from another person.
But with regard to derivative acquisition, it may be otherwise, for the person from whom the thing is acquired may not have an unlimited right to it, or he may convey or transfer it with certain reservations of right.
Derivative conveyances are those which presuppose some other precedent conveyance, and serve only to enlarge, confirm, alter, restrain, restore, or transfer the interest granted by such original conveyance.
www.lectlaw.com /def/d143.htm   (184 words)

 PlanetMath: directional derivative   (Site not responding. Last check: 2007-10-22)
See Also: partial derivative, derivative, derivative notation, Jacobian matrix, gradient, fixed points of normal functions, Hessian matrix
derivative with respect to a vector, partial derivative with respect to a vector
This is version 11 of directional derivative, born on 2001-11-14, modified 2005-04-16.
planetmath.org /encyclopedia/DerivativeWithRespectToAVector.html   (102 words)

 Chilling Effects Clearinghouse: Derivative Works
Whether the first artist has a viable copyrightviolation cause of action against the second artist for violating her right to produce derivative works turns on whether the second artist's appropriation of the first artist's material constitutes fair use.
In short, a derivative work is a whole work based on one or more other whole works.
If you received a cease and desist letter claiming your art is an unauthorized derivative work, this information should help you understand the law to which the letter refers.
www.chillingeffects.org /derivative   (765 words)

 Derivative Instrument
is a derivative because it derives its value from the value of a stock.
One is the distinction between linear and non-linear derivatives.
Kolb (2002) is a practical introduction to derivatives.
www.riskglossary.com /articles/derivative_instrument.htm   (528 words)

 A Looming Financial Derivatives Crisis
The Comptroller of the Currency guesses that the national amount of derivatives in the portfolios of U.S.-based banks is $28.2 trillion, of which 95% is held by the eight largest banks and their off-balance sheet exposure is 243% of their risk based capital.
Banks have gotten filthy rich off derivatives and, of course, cheap give away money from the FED. Born says, "we are the only federal agency with statutory authority to regulate hedge funds and a certain portion of the swaps market" and she is right.
Derivative protection bought from Russian banks to protect investments is worthless since the government declared a 90-day moratorium and there is no reference rate for the ruble.
www.usagold.com /DerivativesChapman.html   (4649 words)

 Untitled Document
In the previous sections we have discussed how the derivative is related to the slope of the tangent line for a curve at a point.
This was viewed geometrically by considering a sequence of secant lines that approached the tangent line at a point or algebraically by examining what happened to the slope computed at a point as you took points closer and closer together on the curve.
In the previous sections, we noted that the derivative at a point on a curve is the slope of the tangent line at that point.
www-rohan.sdsu.edu /~jmahaffy/courses/s00/math121/lectures/limits_cont_deriv/limits.html   (809 words)

The derivative itself is merely a contract between two or more parties.
There are even derivatives based on weather data, such as the amount of rain or the number of sunny days in a particular region.
Derivatives are generally used to hedge risk, but can also be used for speculative purposes.
www.investopedia.com /terms/d/derivative.asp   (403 words)

 Covariant derivative: Facts and details from Encyclopedia Topic   (Site not responding. Last check: 2007-10-22)
In differential geometry, a connection (also connexion) or covariant derivative is a way of specifying a derivative of a vector field along...
The covariant derivative of a tensor field along a vector field v is again a tensor field of the same type.
In words: the covariant derivative is the normal derivative along the coordinates along with correction terms which tell how the coordinates change.
www.absoluteastronomy.com /encyclopedia/c/co/covariant_derivative.htm   (2507 words)

 Copyright Registration and Derivative Works
A derivative work is one that is based, in whole or in part, on a pre-existing work (or numerous works).
When an original author and an author of a derivative work are different, their respective rights are generally addressed by a contract between them.
The practitioner representing a plaintiff pursuing infringement of an unregistered derivative work, when the original work was registered, still may have legal grounds to proceed, depending on the forum.
www.oblon.com /Pub/HudisSullivanCopyrightArticle.html   (2167 words)

 Derivative Works | Linux Journal
A ``derivative work'' is a work based upon one or more pre-existing 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.
If the FSF claimed these to be derivative works too, THEN I would happily agree with them on their licensing, because it would be consistent, as using the other software in ANY way woudl be a derivative work, but according to them using it one way is a derivative, but using it another, is not.
The way they worked internally was completely different and one was not derived from the other in any way, except by locking a group of people in a room and asking them to write a spec for a processor that did the same thing as the existing Intel processor.
linuxjournal.com /article.php?sid=6366   (9261 words)

 What is a derivative?
In the lexical database, a derivative is usually entered as a subentry.
A derivative is a stem that is formed by combining a root with an affix that adds a component of meaning that is more than just inflectional.
A derivative is a stem formed by derivation, a morphosyntactic operation.
www.sil.org /linguistics/GlossaryOfLinguisticTerms/WhatIsADerivative.htm   (111 words)

 U.S. Copyright Office - Information Circular
A “derivative work,” that is, a work that is based on (or derived from) one or more already existing works, is copyrightable if it includes what the copyright law calls an “original work of authorship.” Derivative works, also known as “new versions,” include such works as translations, musical arrangements, dramatizations, fictionalizations, art reproductions, and condensations.
A work that has fallen in the public domain, that is, which is no longer protected by copyright, may be used for a derivative work, but the copyright in the derivative work will not restore the copyright of the public domain material.
The appropriate application form to use to register a claim to copyright in a derivative work depends upon the type of work for which registration is sought.
www.copyright.gov /circs/circ14.html   (1927 words)

 Derivative Formulas
                                       The derivative of a constant is zero.
                            The Derivative of e raised to a variable.
                     The Derivative of a constant raised to a variable.
www.pen.k12.va.us /Div/Winchester/jhhs/math/lessons/calculus/deriv2.html   (72 words)

 Mathlets: Derivative Calculator
Calculates the derivative of an expression specified using a simple expression syntax.
The result of one derivative evaluation step will be entered back into the text input field.
The button next to the "Variable" label displays a pop-up menu which can be used to select a variable for partial derivatives.
cs.jsu.edu /mcis/faculty/leathrum/Mathlets/derivcalc.html   (240 words)

 The Second Derivative
If we remember that the derivative of a function tells us whether the function is increasing or decreasing, then we are now interested in the derivative of the derivative which we generally call the second derivative.
The second derivative being positive implies that the graph is concave up since the slope of tangent lines must be increasing.
When the second derivative is negative, it implies that the graph is concave down since the slope of tangent lines must be decreasing.
www.ugrad.math.ubc.ca /coursedoc/math100/notes/apps/second-deriv.html   (715 words)

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