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In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much a quantity is changing at a given point. For example, the derivative of the position (or distance) of a vehicle with respect to time is the instantaneous velocity (respectively, instantaneous speed) at which the vehicle is travelling. Conversely, the integral of the velocity over time is the vehicle's position.

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Identical vs derivative reuse : The Rockley Blog

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Wikipedia About Derivative

In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much a quantity is changing at a given point. For example, the derivative of the position (or distance) of a vehicle with respect to time is the instantaneous velocity (respectively, instantaneous speed) at which the vehicle is travelling. Conversely, the integral of the velocity over time is the vehicle's position.

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. A closely related notion is the differential of a function.

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

Differentiation and the derivative

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Differentiation is a method to compute the rate at which a dependent output y, changes with respect to the change in the independent input x. This rate of change is called the derivative of y with respect to x. In more precise language, the dependence of y upon x means that y is a function of x. If x and y are real numbers, and if the graph of y is plotted against x, the derivative measures the slope of this graph at each point. This functional relationship is often denoted y = ƒ(x), where ƒ denotes the function.

The simplest case is when y is a linear function of x, meaning that the graph of y against x is a straight line. In this case, y = ƒ(x) = m x + c, for real numbers m and c, and the slope m is given by

m={\mbox{change in } y \over \mbox{change in } x} = {\Delta y \over{\Delta x}}

where the symbol Δ (the uppercase form of the Greek letter Delta) is an abbreviation for "change in." This formula is true because

y + Δy = ƒ(x+ Δx) = m (x + Δx) + c = m x + c + m Δx = y + mΔx.

It follows that Δy = m Δx.

This gives an exact value for the slope of a straight line. If the function ƒ is not linear (i.e. its graph is not a straight line), however, then the change in y divided by the change in x varies: differentiation is a method to find an exact value for this rate of change at any given value of x. The idea, illustrated by Figures 1-3, is to compute the rate of change as the limiting value of the ratio of the differences Δy / Δx as Δx becomes infinitely small.

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News about Derivative

Berkshire Hathaway reports a $1.5B 1Q loss

AP via Yahoo! NewsWarren Buffett's company reported a $1.5 billion first-quarter loss as it wrote down its ConocoPhillips investment and mostly unrealized derivative losses helped drag Berkshire Hathaway's results below last year's $940 million profit.http://news.yahoo.com/s/ap/20090509/ap_on_bi_ge/us_earns_ber...

Milan Placed Derivative Bet on Italy Default, Court Papers Show

BloombergMay 8 (Bloomberg) -- Milan city officials sold derivatives betting against an Italian government default after being persuaded by bankers at JPMorgan Chase & Co.http://www.bloomberg.com/apps/news?pid=20601009&sid=aYDXWruC...

China Interest-Rate Swaps Fall to One-Month Low on Deflation

BloombergMay 11 (Bloomberg) -- China’s six-year interest-rate swaps dropped to the lowest in more than a month after the government said deflation accelerated in April, prompting traders to pare expectations for the pace of the economy’s recovery.http://www.bloomberg.com/apps/news?pid=20601080&sid=abCnsXCf...

Indian Bonds Decline as Some Investors Sold Before Debt Sales

BloombergMay 11 (Bloomberg) -- Indian bonds fell for a third day on speculation some investors sold part of their holdings to raise cash for purchases at bond auctions later this week.http://www.bloomberg.com/apps/news?pid=20601091&sid=aN2bmZKJ...

U.K. Pledges Insolvency Law Overhaul After Lehman Collapse

BloombergMay 11 (Bloomberg) -- The U.K. Treasury will call for faster payments to creditors and greater clarity on trades in the event an investment bank collapses, according to a person with knowledge of the plans.http://www.bloomberg.com/apps/news?pid=20601009&sid=a1Czylvc...

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Dealers to Meet NY Fed Reconciliation Requirements as TriOptima ...

Consumer Electronics NetNEW YORK, BUSINESS WIRE -- TriOptima announced that its portfolio reconciliation service, triResolve, is now regularly reconciling more than 50 percent of all collateralised OTC derivative transactions globally, up from 40 percent in June. The ... http://www.consumerelectronicsnet.com/articles/viewarticle.j...

Snow sweeps through northern Utah

ksl.comWith respect to any content that you submit, you grant to KSL an irrevocable, perpetual, worldwide, royalty-free, fully assignable license to use, reproduce, modify, publish, translate, create derivative works from, distribute, sublicense, perform ... http://www.ksl.com/?nid=148&sid=4508016&comments=true

Australian Personal Finance Down 5.2% In August Vs July

FXStreet.comIf you are an individual, you agree not to store, copy, reproduce, modify, distribute, transmit, display, perform, publish, transfer, create derivative works from, broadcast or circulate any Dow Jones content to anyone, including but not limited to ... http://www.fxstreet.com/news/forex-news/article.aspx?StoryId...

Ambac Releases Selected Monthly Data for August 2008

ForbesAs such, the monthly data does not reflect the results of the quarterly credit derivative impairment, insurance loss reserve and investment portfolio impairment analysis. Key Financial Highlights: -- Ambac discussed the impact of SFAS 157 on the ... http://www.forbes.com/businesswire/feeds/businesswire/2008/1...

Indian shares plummet on U.S. recession fears, global slowdown worries

CNBCP-notes are offshore derivative instruments used by foreign investors to buy Indian shares and debt instruments without disclosing their identities. tfn.newsdesk@thomsonreuters.com aka/jro COPYRIGHT Copyright Thomson Financial News Limited 2008. All ... http://www.cnbc.com/id/27046140

Search results for Derivative

derivative - definition of derivative by the Free Online Dictionary ...

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Derivative

Derivative - Definition of Derivative on Investopedia - In finance, a security whose price is dependent upon or derived from one or more underlying assets. The ... http://www.investopedia.com/terms/d/derivative.asp

The Derivative

The Partial Derivative. 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 ... http://hyperphysics.phy-astr.gsu.edu/hbase/deriv.html

derivative - Wiktionary

The translations below need to be checked and inserted above into the appropriate translation tables, removing any numbers. Numbers do not necessarily match those in definitions.http://en.wiktionary.org/wiki/derivative

Derivative - Visual Thinking

Derivative provides software tools for designing and performing visuals for the electronic music culture, and for media artists who create interactive 3D artworks. Derivative is ... http://www.derivativeinc.com/Home/Home.asp
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I Will Derive!

I Will Derive!I parody of "I Will Survive" that I did with a couple of my friends for our Calculus and Physics classes. Lyrics: At first I was afraid, what could the answer be? It said given...Flash - Video

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Where are Derivatives Heading?Stefan Armbruster, director global equity derivative at Deutsche Bank, discusses the direction for the derivatives markets for early 2008.Flash - Video

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Answers for Derivative

Kittyderivative?KittyRewriting: y = x(16-x^2)^1/2 dy/dx = [(16-x^2)^1/2]d/dx(x) + xd/dx[(16-x^2)^1/2] chain rule y' = [(16-x^2)^1/2](1) + x[(1/2)(16-x^2)^(-1/2)](-2x) = sqr(16-x^2) - 2(x^2)/sqr(16-x^2) Try the ...ranafantasmaWhat is the second derivative of the area of a circle with respect to r?ranafantasmaThe second derivative would be the number of radians in a circle. 2pi radians is the same as 360 degrees.venomfxWhat is the meaning of the second derivative of the volume of a sphere with repect to it's radius?venomfxIt is the rate at which the surface area grows with growing R (or shrinks with shrinking R). Regarding Helmut's answer: If instead of using x for the cube, you use the radius of the inscribed sphe...MaddieWhat is the derivative of the volume of a triangular cylinder?MaddieTsk,Maddie, V = 16 * h * [h/2] {similar triangles}, find dh / dt when you know dV / dt, evaluate with h = 4.Julia BHow to find the derivative from tangent lines?Julia BTangent lines alone are meaningless if you don't know a point (x1,y1) on each line. If you have enough tangents, that is the slope of a curve at specific values of x and y, and if the points are c...
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