Refimprove date October 2010 Financial markets In finance , a derivative is a financial instrument whose ... create option finance option ability where the value of the derivative is linked to a specific ... hands and is thus referred to as notional. over the counter finance Over the counter OTC derivative ... http derivatives litigation.blogspot.com Derivatives Litigation DEFAULTSORT DerivativeFinance ..., with the most common being Swap finance swaps , Futures contract futures , and Option finance options . Derivatives are a form of alternative investment . A derivative is not a stand alone asset ... categorized by the relationship between the underlying asset and the derivative e.g., forward contract forward , option finance option , swap finance swap the type of underlying asset e.g., equity derivative s, foreign exchange derivative s, interest rate derivative s, commodity derivatives or credit derivatives the market in which they trade e.g., exchange traded or Over the counter finance ... 2011 Derivatives are used by investors to provide Leverage finance leverage or gearing , such that a small movement in the underlying value can cause a large difference in the value of the derivative ..., moves in a given direction, stays in or out of a specified range, reaches a certain level Hedge finance hedge or mitigate risk in the underlying, by entering into a derivative contract whose value moves ... date October 2010 Derivatives can be considered as providing a form of insurance in Hedge finance ... a clearing house finance clearing house , insures a futures contract, not all derivatives are insured ... against risk. Thus, some individuals and institutions will enter into a derivative contract to speculate ... price according to a derivative contract when the future market price is high, or to sell an asset in the future at a high price according to a derivative contract when the future market price is low ... Financial instrument In broad terms, there are two groups of derivative contracts, which are distinguished ... more details
, see Differential calculus . For other uses, see Derivative disambiguation . File Tangent ... line to that function, drawn in red. The slope of the tangent line is equal to the derivative ... , the derivative is a measure of how a function mathematics function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity for example, the derivative of the position of a moving object ... to the time when the integral ends. The derivative of a function at a chosen input value describes ... real variable, the derivative at a point equals the slope of the tangent line to the graph of a function graph of the function at that point. In higher dimensions, the derivative of a function ... a derivative is called differentiation . The reverse process is called antiderivative antidifferentiation ... variable calculus. Differentiation and the derivative File Graph of sliding derivative line.gif left thumb 400px Click for larger image At each point, the derivative of math scriptstyle f x 1 x sin x ... to the blue curve its slope is the derivative. Note derivative is positive number positive where ... input x . This rate of change is called the derivative of y with respect to x . In more precise ... number s, and if the graph of a function graph of y is plotted against x , the derivative measures ... in x is denoted by dx , and the derivative of y with respect to x is written math frac dy dx , math suggesting the ratio of two infinitesimal quantities. The above expression is read as the derivative ... did not pass straight through the graph. The derivative of y with respect to x at a is, geometrically ... x frac f x h f x h . math This expression is Isaac Newton Newton s difference quotient . The derivative ..., the derivative of the function at a is the limit of a function limit math f a lim h to 0 frac f a h ... notations for the derivativeDerivative Notations for differentiation see below . Equivalently, the derivative ... more details
wiktionarypar derivativeDerivative , in calculus, is a measurement of how a function changes when the values of its inputs change. Derivative may also refer to Derivativefinance , a contract whose value is derived from that of other quantities Derivative chemistry , a type of compound which is a product of the process of derivatization Derivative Inc., a spin off of Side Effects Software, creators of Houdini software Derivative suit or derivative action, a type of lawsuit filed by minority shareholders Derivative work , in copyright law, a modification of an original work Formal derivative , in mathematics, an operation on elements of a polynomial ring which mimics the form of the derivative from calculus Aeroderivative gas turbine , a mechanical drive gas turbine derived from an aero engine gas turbine See also Derivation disambiguation Derived , in phylogenetics, a trait present in an organism, but absent in the last common ancestor of its group Disambig bg cs Deriv t da Derivat de Derivat eo Deriva o fr D riv homonymie is Aflei a he lb Derivat nl Derivaat pl Pochodna ujednoznacznienie ru sk Deriv t th Derivative tr T rev anlam ayr m ... more details
Orphan date February 2009 Derivative Dribble is a blog written by Charles Davi focused on finance , particularly Derivativefinance derivatives and structured products . The site explains how various financial instruments work and why they are used. Additionally, the site has many opinion pieces on how derivatives and structured products operate in the broader financial system . Recognition The site is widely referenced in leading finance blogs ref http ftalphaville.ft.com blog 2008 12 08 50142 further reading 170 ref ref http acrossthecurve.com ?s Derivative Dribble ref ref http paul.kedrosky.com archives 2008 12 09 afternoon readi.html ref and is syndicated on the Atlantic Monthly s Business Channel ref http business.theatlantic.com author charles davi ref and Nouriel Roubini s RGE Monitor ref http www.rgemonitor.com globalmacro monitor author name cdavi3 Charles Davi ref . External links http www.derivativedribble.wordpress.com Derivative Dribble References Reflist Category Blogs ... more details
nofootnotes date March 2009 In finance , inflation derivative or inflation indexed derivatives refers to an over the counter finance over the counter and exchange traded derivativefinancederivative that is used to transfer inflation risk from one counterparty to another. Typically, Interest rate swap real rate swaps also come under this bracket, such as asset swap s of inflation indexed bond s government issued inflation indexed bonds, such as the Treasury Inflation Protected Securities , UK inflation linked gilt edged securities ILGs , French OATeis, Italian BTPeis, German Bundeis and Japanese JGBi s are prominent examples . Inflation swap s are the linear form of these derivatives. They can take a similar form to fixed versus floating interest rate swaps which are the derivative form for fixed rate bonds , but use a real rate coupon versus Public float floating , but also pay a redemption pickup at Maturity finance maturity i.e., the derivative form of inflation indexed bond s . Inflation swap s are typically priced on a Zero coupon bond zero coupon basis ZC like ZCIIS for example , with payment exchanged at the end of the term. One party pays the compounded fixed rate and the other the actual inflation rate for the term. Inflation swaps can also be paid on a year on year basis YOY like YYIIS for example where the year on year rate of change of the price index is paid, typically yearly as in the case of most European YOY swaps, but also monthly for many swapped notes in the US ... rate. Option finance Options on inflation including Interest rate cap and floor interest rate caps ... pickup at Maturity finance maturity is exchanged for interest rate payments expressed as a Risk ... Finance. ISBN 0 470 86812 0. Brigo, Damiano and Fabio Mercurio Interest Rate Models Theory and Practice, with Smile, Inflation, and Credit 2nd edition, 2006 Springer Finance. ISBN 3 540 22149 2. Derivatives market Category Derivatives finance Category Interest rates ... more details
In finance , an equity derivative is a class of Derivativefinance derivatives whose value is at least partly derived from one or more underlying Stock equity securities . Option finance Options and Future finance futures are by far the most common equity derivatives, however there are List of finance topics Equity derivatives many other types of equity derivatives that are actively traded. Equity options main Option finance Equity options are the most common type of equity derivative. ref http www.investopedia.com terms e equity derivative.asp Investopedia.com Equity derivatives ref They provide the right, but not the obligation, to buy call or sell put a quantity of stock 1 contract 100 shares of stock , at a set price strike price , within a certain period of time prior to the expiration date . Warrants main Warrant finance In finance , a warrant is a security finance security that entitles the holder to buy stock of the company that issued it at a specified price, which is much lower than the stock price at time of issue. Warrants are frequently attached to bonds or preferred stock as a sweetener, allowing the issuer to pay lower interest rates or dividends. They can be used to enhance the yield finance yield of the bond, and make them more attractive to potential buyers. Convertible bonds main Convertible bond Convertible bonds are bonds that can be converted into shares of stock in the issuing types of companies company , usually at some pre announced ratio. It is a hybrid security with debt and equity like features. It can be used by investors to obtain the upside of equity ... . A typical example of this type of derivative is the Contract for difference CFD where one party gains exposure to a share price without buying or selling the underlying Share finance share ... derivatives Other examples of equity derivative securities include exchange traded fund s and Intellidex es. References Reflist 2 Derivatives market Category Derivatives finance Category Options zh ... more details
growth and exponential decay are processes with constant logarithmic derivative. In mathematical finance ... derivative of a function mathematics function f is defined by the formula math frac f f math where f &prime is the derivative of f . When f is a function f x of a real variable x , and takes real numbers real , strictly Positive number positive values, this is equal to the derivative of ln f or, the derivative of the natural logarithm of f . This follows directly from the chain rule . The logarithmic derivative of f is equal to the natural logarithm of the geometric derivative of f . See ... also apply to the logarithmic derivative, even when the function does not take values in the positive ... derivative of a product is the sum of the logarithmic derivatives of the factors. But we can also use the Leibniz law for the derivative of a product to get math frac uv uv frac u v uv uv frac u u frac v v . math Thus, it s true for any function that the logarithmic derivative of a product ... this is a consequence , the logarithmic derivative of the reciprocal of a function is the negation of the logarithmic derivative of the function math frac 1 u 1 u frac u u 2 1 u frac u u , math just .... More generally, the logarithmic derivative of a quotient is the difference of the logarithmic .... Generalising in another direction, the logarithmic derivative of a power with constant real exponent is the product of the exponent and the logarithmic derivative of the base math frac ... each pair of rules is related through the logarithmic derivative. Computing ordinary derivatives ... it directly, we compute its logarithmic derivative. That is, we compute math frac f f frac u u frac ... makes it possible to compute Nowrap &fnof by computing the logarithmic derivative of each factor, summing, and multiplying by . Integrating factors The logarithmic derivative idea is closely connected ... operator by the logarithmic derivative G &prime G . In practice we are given an operator ... more details
A fund derivative is a financial structured product related to a Collective investment scheme fund , normally using the underlying fund to determine the payoff. This may be a private equity fund , mutual fund or hedge fund . Purchasers obtain exposure to the underlying fund or funds whilst improving their risk profile over a direct investment. For example the purchaser may be attracted by a fund s star manager, performance history or strategy, whilst improving their counterparty risk and getting leverage, currency hedging or a capital guarantee via the derivative. The structured product may be investible by retail clients or institutional investors that would not otherwise buy the fund, because of its provision of safeguard features such as capital guarantees or the appointment of independent administrators to calculate the underlying fund s value and additional oversight mechanisms. Typical fund derivatives might be a call option on a fund, a CPPI on a fund, or a leveraged note on a fund. More complicated structures might include auto call features guaranteeing that if the derivative reached a certain value that value was locked in, on top of an initial minimum value guarantee at issuance. Maturities might range from three to ten years, or more rarely multiple decades. The big players in this field are investment banks such as Barclays , BNP Paribas , Citigroup , Credit Suisse , Deutsche Bank , Goldman Sachs , Soci t G n rale . Fund derivatives have had explosive growth over the past 10 years but are still a major growth area. New structures are constantly being developed to suit market and client opportunities. External links http www.barcap.com Client offering Global Markets Equities Trade Insight and Execution Equity Derivatives Fund Linked Fund linked Derivatives http www.altrus.com Nomura wins Silver Award for Best Hedge Fund Linked Certificate derivatives market Category Private equity Category Derivatives finance private equity stub ... more details
Cleanup date July 2008 In finance , a credit derivative is a securitization securitized derivativefinancederivative whose value is derived from the credit risk on an underlying bond, loan or any other ... Bond market Financial risk DEFAULTSORT Credit Derivative Category Derivatives finance de Kreditderivat ...?id 4234&nid 1575 title PLC Finance Practice Note Credit Derivatives by Edmund Parker ref Credit ... entity will default on one of its obligations such as a bond or loan default finance obligation ... as an unfunded credit derivative. If the credit derivative is entered into by a financial institution or a special purpose vehicle SPV and payments under the credit derivative are funded using securitization ... these obligations, this is known as a funded credit derivative. This synthetic securitization .... Market size and participants Credit default products are the most commonly traded credit derivative product ref name BBACDR cite web url http www.bba.org.uk content 1 c4 76 71 Credit derivative report ... . ref cite news url http business.timesonline.co.uk tol business industry sectors banking and finance ... categories funded credit derivatives and unfunded credit derivatives. An unfunded credit derivative ... itself without recourse to other assets. A funded credit derivative involves the protection seller the party ... seller s default. It is also known as counterparty risk. Unfunded credit derivative products include ... transaction Credit Spread Option CDS index products Funded credit derivative products include the following ... credit derivative products Credit default swap Main Credit default swap The credit default swap ... it isolates both credit risk and market risk. Key funded credit derivative products Credit linked ... be through the use of a credit derivative, but does not have to be. Credit linked note s CLN Credit ... asset, or assets. This link may be through the use of a credit derivative, but does not have ... main collateralized debt obligation Collateralized debt obligations CDOs are a form of credit derivative ... more details
derivative markets Risk Management Hedging Speculation Trading Investment Portfolio Diversification ... rise in the jet price for the period is protected by the derivative transaction. A cash settlement ... Investopedia article on energy derivatives DEFAULTSORT Energy Derivative Category Derivatives finance Category Energy economics ... more details
for the Slovenian newspaper Finance newspaper multiple issues prose January 2008 refimprove June 2007 rewrite February 2008 Finance sidebar Finance pronounced f n nts or fa n nts is the science of funding funds management. ref Gove, P. et al. 1961. Finance. Webster s Third New International Dictionary ... areas of finance are business finance , personal finance , and public finance . ref finance ... www.britannica.com EBchecked topic 207147 financeFinance ref Finance includes saving money and often includes lending money. The field of finance deals with the concepts of time , money , risk and how they are interrelated. It also deals with how money is spent and budgeted. One facet of finance ... of Credit finance credit , although private equity , mutual funds , hedge funds , and other organizations ... assets to be trader finance traded on securities exchange s such as stock exchange s, including debt such as bond finance bonds as well as Stock equity in public company publicly traded corporations ... States and Bank of England in the United Kingdom , are strong players in public finance .... Finance is used by individuals personal finance , by governments public finance , by businesses corporate finance and by a wide variety of other organizations, including schools and non profit ... setting. Finance is one of the most important aspects of business management and includes decisions related to the use and acquisition of funds for the enterprise. In corporate finance, a company s capital ... . Personal finance Main Personal finance Questions in personal finance revolve around How much ... finance Main Corporate finance Managerial finance Managerial or corporate finance is the task of providing ... finance Small and Medium Enterprises . It generally involves balancing risk and profitability, while ... by ownership equity and long term credit finance credit , often in the form of Bond finance bonds ... finance is investment, or fund management . An investment is an acquisition of an asset in the hope ... more details
In mathematics In abstract algebra and mathematical logic a derivative algebra abstract algebra derivative algebra is an algebraic structure that provides an abstraction of the derivative operator in topological space topology and which provides algebraic semantics for the modal logic wK3 . In differential geometry a derivative algebra is a vector space with a product operation that has similar behaviour to the standard cross product of 3 vector geometric vector s. Citation needed date July 2009 disambig ... more details
In mathematics , the quasi derivative is one of several generalizations of the derivative of a function mathematics function between two Banach space s. The quasi derivative is a slightly stronger version of the G teaux derivative , though weaker than the Fr chet derivative . Let f A &rarr F be a continuous function from an open set A in a Banach space E to another Banach space F . Then the quasi derivative of f at x sub 0 sub &isin A is a linear transformation u E &rarr F with the following property for every continuous function g 0,1 &rarr A with g 0 x sub 0 sub such that g &prime 0 &isin E exists, math lim t to 0 frac f g t f x 0 t u g 0 . math If such a linear map u exists, then f is said to be quasi differentiable at x sub 0 sub . Continuity of u need not be assumed, but it follows instead from the definition of the quasi derivative. If f is Fr chet differentiable at x sub 0 sub , then by the chain rule , f is also quasi differentiable and its quasi derivative is equal to its Fr chet derivative at x sub 0 sub . The converse is true provided E is finite dimensional. Finally, if f is quasi differentiable, then it is G teaux differentiable and its G teaux derivative is equal to its quasi derivative. References cite book author Dieudonn , J title Foundations of modern analysis publisher Academic Press year 1969 math stub Category Banach spaces Category Generalizations of the derivative pl Quasi pochodna ... more details
Freight Derivative s, which includes Forward freight agreement Forward Freight Agreement FFA , Container Freight Swap Agreement container freight swap agreements and options based on these, are financial instrument s for trading in future levels of freight rates, for dry bulk common carrier carrier s, tank truck tanker s and containerships. These instruments are settled against various freight rate indices published by the Baltic Exchange for Dry and most Wet contracts & Platt s Asian Wet contracts . FFAs are often traded over the counter through broker members of the Forward Freight Agreement Brokers Association FFABA such as Clarkson s Securities, SSY Simpson, Spence and Young, Braemar Seascope LTD, Ifchor, FIS Freight Investor Services, BGC Partners, GFI Group Inc, ACM Shipping Ltd, BRS, Tradition Platou, ICAPHYDE and IMAREX but screen based trading is becoming more popular, through various screens. Trades can be given up for clearing by the broker to one of the clearing houses that support such trades. There are four clearing houses for freight Imarex NOS Clearing , LCH.Clearnet , NYMEX NY Mercantile Exchange and SGX Singapore Stock Exchange Singapore . Freight derivatives are primarily used by shipowners and operators, oil companies, trading companies and grain houses as tools for managing freight rate risk. Recently with Commodities now standing at the forefront of international economics the large financial trading houses, including banks and hedge funds have entered the market. Dry Freight or Dry Bulk FFAs The Baltic Exchange, Baltic Dry Index which measures the cost for shipping goods like iron ore and grains, doubled over the past 12 months and has risen more than fourfold since 2006. The trading volume of dry freight derivatives, a market estimated to be worth about 200 billion in 2007, grew as those needing ships attempted to contain their risks and investment ... Derivatives finance Category Shipping management de Forward Freight Agreement ... more details
A time derivative is a derivative of a function with respect to time , usually interpreted as the Derivative ... derivative. In addition to the normal Derivative Leibniz s notation Leibniz s notation, math frac ... x math Derivative Newton s notation Newton s notation , and adding a Prime symbol prime to the function, math x t , math Derivative Lagrange s notation Lagrange s notation . These two shorthands are generally ... derivative with respect to time is written as math frac d 2x dt 2 math with the corresponding shorthands of math ddot x math and math x t math . As a generalization, the time derivative of a vector, say ... derivative math dot x math is its velocity , and its second derivative with respect to time, math ddot x math , is its acceleration . Even higher derivatives are sometimes also used the third derivative ... quantities in science are time derivatives of one another force is the time derivative of momentum Power physics power is the time derivative of energy electrical current is the time derivative of electric charge and so on. A common occurrence in physics is the time derivative of a vector geometric vector , such as velocity or displacement. In dealing with such a derivative, both magnitude and orientation .... The time derivative of the displacement vector is the velocity vector. In general, the derivative of a vector is a vector made up of components each of which is the derivative of the corresponding ... y, x cdot x, y yx xy 0 , . math Acceleration is then the time derivative of velocity math mathbf a t frac ... situation involves a stocks and flows stock variable and its time derivative, a stocks and flows flow variable . Examples include The flow of net fixed investment is the time derivative of the capital stock . The flow of inventory investment is the time derivative of the stock of inventories . The growth rate of the money supply is the time derivative of the money supply divided by the money supply itself. Sometimes the time derivative of a flow variable can appear in a model The growth rate ... more details
In mathematics , the covariant derivative is a way of specifying a derivative along tangent vector s of a manifold . Alternatively, the covariant derivative is a way of introducing and working with a connection ... Euclidean space, the covariant derivative can be viewed as the orthonormal projection of the Euclidean derivative along a tangent vector onto the manifold s tangent space. In this case the Euclidean derivative is broken into two parts, the extrinsic normal component and the intrinsic covariant derivative component. This article presents an introduction to the covariant derivative of a vector ... system and the traditional index notation. The covariant derivative of a tensor field is presented as an extension of the same concept. The covariant derivative generalizes straightforwardly to a notion ... . Introduction and history Historically, at the turn of the 20th century, the covariant derivative ... a notion of derivative differentiation which generalized the classical directional derivative of vector fields on a manifold. This new derivative the Levi Civita connection was Covariance and contravariance ... , 325 412. ref that a covariant derivative could be defined abstractly without the presence of a metric ... law could serve as a starting point for defining the derivative in a covariant manner. Thus the theory ... the classical notion of covariant derivative in many post 1950 treatments of the subject. Motivation The covariant derivative is a generalization of the directional derivative from vector calculus . As with the directional derivative, the covariant derivative is a rule, math nabla bold u bold ... , defined in a neighborhood of P . ref The covariant derivative is also denoted variously by math ... bold u bold v P math , also at the point P . The primary difference from the usual directional derivative ... transformation . The covariant derivative is required to transform, under a change in coordinates, in the same way as a vector does the covariant derivative must change by a covariant transformation ... more details
In mathematics , the symmetric derivative is an Operator mathematics operation related to the ordinary derivative . It is defined as math lim h to 0 frac f x h f x h 2h . math A function is symmetrically differentiable at a point x if its symmetric derivative exists at that point. It can be shown that if a function is differentiable function differentiable at a point, it is also symmetrically differentiable, but the converse is not true. The best known example is the absolute value function f x x , which is not differentiable at x 0, but is symmetrically differentiable here with symmetric derivative 0. It can also be shown that the symmetric derivative at a point is the mean of the one sided derivatives at that point, if they both exist. See also Symmetrically continuous function References cite book first Brian S. last Thomson year 1994 title Symmetric Properties of Real Functions publisher Marcel Dekker isbn 0 8247 9230 0 Category Differential calculus math stub bs Simetri na derivacija ca Derivada sim trica eo Simetria deriva o pt Derivada sim trica ... more details
The material derivative ref name BSLr2 ref name Batchelor cite book first G.K. last Batchelor authorlink ... Press isbn 0521663962 p. 72&ndash 73. ref is a derivative taken along a path moving with velocity ... of the fluid. Then the material derivative describes the temperature evolution of a certain fluid ... trajectory while following the fluid flow. The material derivative can serve as a link between Continuum ... derivative ref name Ockendon cite book first H. last Ockendon coauthors Ockendon, J.R. title Waves and Compressible Flow publisher Springer year 2004 isbn 038740399X p. 6. ref advective derivative substantive derivative ref name Granger cite book first R.A. last Granger title Fluid Mechanics publisher Courier Dover Publications year 1995 isbn 0486683567 p. 30. ref substantial derivative ref name ... 8 p. 83. ref Lagrangian derivative ref name Mellor cite book first G.L. last Mellor title Introduction to Physical Oceanography publisher Springer year 1996 isbn 1563962101 p. 19. ref Stokes derivative ref name Granger particle derivative hydrodynamic derivative ref name BSLr2 derivative following the motion ref name BSLr2 total derivative ref name BSLr2 Definition The material derivatives of a scalar ... math is the gradient of a scalar, while math nabla mathbf u math is the covariant derivative of a vector. In case of the material derivative of a vector field, the term v u can both be interpreted as v u involving the tensor derivative continuum mechanics tensor derivative of u , or as v u , leading ... derivative is both used for the whole material derivative D&phi Dt or D u Dt , and for only the spatial ... derivative only equals D Dt for time independent flows. These derivatives are physical ... by the vector field v x , t . The total derivative with respect to time of &phi is expanded through ... varphi cdot frac d mathbf x d t math It is apparent that this derivative is dependent on the vector ... a chosen path x t in space. For example, if math d mathbf x d t 0 math is chosen, the time derivative ... more details
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 derivative calculus . Though they appear similar, the algebraic advantage of a formal derivative is that it does not rely on the notion of a limit mathematics limit , which is in general impossible to define for a ring mathematics ring . Many of the properties of the derivative are true of the formal derivative, but some, especially those that make numerical statements, are not. The primary use of formal differentiation in algebra is to test for multiple roots of a polynomial . Definition The definition of a formal derivative is as follows fix a ring R not necessarily commutative and let A R x be the ring of polynomials over R . Then the formal derivative is an operation on elements of A , where if math f x , ,a n x n cdots a 1 x a 0 math then its formal derivative is math f x , ,Df x n a n x n 1 cdots 2 a 2 x a 1 math just as for polynomials over the real numbers real or complex numbers complex numbers. Properties It can ... also be included as a linearity property. The formal derivative satisfies the Product rule Leibniz ... . Application to finding repeated factors As in calculus, the derivative detects multiple roots ... however, its formal derivative is zero since 3 0 in R and in any extension of R , so when we pass ... to analytic derivative When the ring R of scalars is commutative, there is an alternative and equivalent definition of the formal derivative, which resembles the one seen in differential calculus ... with the formal derivative of f as it was defined above. This formulation of the derivative ... Y math continuous at math X math , it will recapture the classical definition of the derivative. If it is carried .... This way differentiation becomes a part of algebra of functions. See also Derivative ... derivative References Lang Algebra edition 3r Category Abstract algebra pl Pochodna formalna http ... more details
The derivative is a fundamental construction of differential calculus and admits many possible generalizations ... case is the functional derivative variational derivative in the calculus of variations . Repeated ... calculus main Fr chet derivative The derivative is often met for the first time as an operation ... x h math exists. Its value is then the derivative x . A function is differentiable on an Interval ... L z f x z f x x f x math is tangent to the original function at the point math x, f x math , the derivative ... case coincides with the original definition. In this case the derivative is represented by a 1 by 1 ... of this matrix represents a partial derivative , specifying the rate of change of one range coordinate ... from R sup n sup to R scalar field s , the total derivative can be interpreted as a vector field ... directional derivative s of Scalar mathematics scalar functions or normal directions. Several linear ... valued functions from R to R sup n sup i.e., parametric curve s , one can take the derivative of each component separately. The resulting derivative is another vector valued function. This is useful, for example, if the vector valued function is the position vector of a particle through time, then the derivative is the velocity vector of the particle through time. The convective derivative takes into account ... The subderivative and subgradient are generalizations of the derivative to convex function s. Higher ... of repeatedly applying the derivative, one repeatedly applies partial derivative s with respect to different ... orders, which are studied in fractional calculus . The 1 order derivative corresponds to the integral ... a Fr chet derivative suitably extended definition of differentiability . The Schwarzian derivative ... way that a normal derivative describes how a function is approximated by a linear map. Functional analysis In functional analysis , the functional derivative defines the derivative with respect to a function of a functional on a space of functions. This is an extension of the directional derivative ... more details
Unreferenced date December 2009 In calculus , the derivative of a constant function is 0 number zero A constant function is one that does not depend on the independent variable, such as f x 7 . The rule can be justified in various ways. The derivative is the slope of the tangent to the given function s graph, and the graph of a constant function is a horizontal line, whose slope is zero. Proof A formal proof , from the Derivative Definition via difference quotients definition of a derivative , is math f x lim h to 0 frac f x h f x h lim h to 0 frac c c h lim h to 0 0 0. math In Leibniz notation , it is written as math frac d dx c 0. math Antiderivative of zero A partial converse to this statement is the following If a function has a derivative of zero on an interval, it must be constant on that interval. This is not a consequence of the original statement, but follows from the mean value theorem . It can be generalized to the statement that If two functions have the same derivative on an interval, they must differ by a constant, or If g is an antiderivative of f on and interval, then all antiderivatives of &fnof on that interval are of the form g x C, where C is a constant. From this follows a weak version of the second fundamental theorem of calculus if is continuous on a,b and g for some function g, then math int a b f x , dx g b g a . math DEFAULTSORT Derivative Of A Constant Category Differential calculus Category Zero ca Derivada d una constant ... more details
In mathematics , the H derivative is a notion of derivative in the study of abstract Wiener space s and the Malliavin calculus . Definition Let math i H to E math be an abstract Wiener space, and suppose that math F E to mathbb R math is Frechet derivative differentiable . Then the Fr chet derivative is a map math mathrm D F E to mathrm Lin E mathbb R math i.e., for math x in E math , math mathrm D F x math is an element of math E math , the dual space to math E math . Therefore, define the math H math derivative math mathrm D H F math at math x in X math by math mathrm D H F x mathrm D F x circ i H to R math , a continuous function continuous linear map on math H math . Define the math H math gradient math nabla H F E to H math by math langle nabla H F x , h rangle H left mathrm D H F right x h lim t to 0 frac F x t i h F x t math . That is, if math j E to H math denotes the adjoint of math i H to E math , we have math nabla H F x j left mathrm D F x right math . See also Malliavin derivative References unreferenced date June 2008 Category Generalizations of the derivative Category Measure theory Category Stochastic processes ... more details
Unreferenced date August 2009 Wikify date May 2009 In calculus , a parametric derivative is a derivative that is taken when both the x and y variables traditionally independent variable independent and dependent variable dependent , respectively depend on an independent third variable t , usually thought of as time . For example, consider the set of function mathematics function s where math x t 4t 2 , math and math y t 3t. , math The first derivative of the parametric equation s above is given by math frac frac dy dt frac dx dt frac dot y t dot x t , math where the notation math dot x t math denotes the derivative of x with respect to t , for example. To understand why the derivative appears in this way, recall the chain rule for derivatives math frac dy dx frac dy dt cdot frac dt dx , math or in other words math frac dy dx frac frac dy dt frac dx dt . math More formally, by the chain rule math frac dy dt frac dy dx cdot frac dx dt math and dividing both sides by math frac dx dt math gets the equation above. Differentiating both functions with respect to t leads to math frac dx dt 8t math and math frac dy dt 3, math respectively. Substituting these into the formula for the parametric derivative, we obtain math frac dy dx frac dot y dot x frac 3 8t , math where math dot x math and math dot y math are understood to be functions of t . The second derivative of a parametric equation is given by math frac d 2y dx 2 math math frac d dx left frac dy dx right math math frac d dt left frac dy dx right cdot frac dt dx math math frac d dt left frac dot y dot x right frac 1 dot x math math frac dot x ddot y dot y ddot x dot x 3 math by making use of the quotient rule for derivatives. The latter result is useful in the computation of curvature . See also Derivative generalizations Parametric equation DEFAULTSORT Parametric Derivative Category Differential calculus eo Parametra deriva o ... more details
Image 4 fonctions du second degr .svg right thumb 200px The second derivative of a quadratic function is constant function constant . In calculus , the second derivative of a function mathematics function &fnof is the derivative of the derivative of &fnof . Roughly speaking, the second derivative measures how the rate of change of a quantity is itself changing for example, the second derivative of the position ... at which the velocity of the vehicle is changing. On the graph of a function , the second derivative ... second derivative curves upwards, while the graph of a function with negative second derivative curves downwards. Notation Details Notation for differentiation The second derivative of a function ... for derivatives, the second derivative of a dependent variable y with respect to an independent variable ..., math the derivative of &fnof is the function math f x 3x 2. math The second derivative of &fnof is the derivative ... derivative of a function &fnof measures the concavity of the graph of &fnof . A function whose second derivative is positive will be concave up sometimes referred to as convex , meaning that the tangent line will lie below the graph of the function. Similarly, a function whose second derivative ... derivative of a function changes sign, the graph of the function will switch from concave down to concave ... derivative is continuous, it must take a value of zero at any inflection point, although not every point where the second derivative is zero is necessarily a point of inflection. Second derivative test main Second derivative test The relation between the second derivative and the graph can be used ... x math . If math f prime prime x 0 math , the second derivative test says nothing about the point math x math , a possible inflection point. The reason the second derivative produces these results ... to write a single Limit mathematics limit for the second derivative math f x lim h to 0 frac ... sequences . Quadratic approximation Just as the first derivative is related to linear approximation ... more details
lowercase In mathematics , in the area of combinatorics , the q derivative is a q analog of the ordinary derivative . Definition The q derivative of a function f x is defined as math left frac d dx right q f x frac f qx f x qx x . math It is also often written as math D qf x math . The q derivative is also known as the Jackson derivative . It is a linear operator math displaystyle D q f x g x D q f x D q g x . math It has product rule analogous to the ordinary derivative product rule which has two equivalent forms math displaystyle D q f x g x g x D q f x f qx D q g x g qx D q f x f x D q g x . math Similarly it satisfies a quotient rule math displaystyle D q f x g x frac g x D q f x f x D q g x g qx g x , quad g x g qx neq 0. math There is also a rule, similar to the chain rule for ordinary derivatives. Let math g x c x k math . Then math displaystyle D q f g x D q k f g x D q g x . math Relationship to ordinary derivatives Q differentiation resembles ordinary differentiation, with curious differences. For example, the q derivative of the monomial is math left frac d dz right q z n frac 1 q n 1 q z n 1 n q z n 1 math where math n q math is the q bracket of n . Note that math lim q to 1 n q n math so the ordinary derivative is regained in this limit. The n th derivative of a function may be given as math D n q f 0 frac f n 0 n frac q q n 1 q n frac f n 0 n n q math provided that the ordinary n th derivative of f exists at x 0. Here, math q q n math is the q Pochhammer symbol , and math n q math is the q factorial . If math f x math is analytic we can apply the Taylor formula to the definition of math D q f x math to get math displaystyle D q f x sum k 0 infty frac q 1 k k 1 x k f k 1 x . math See also Derivative generalizations Jackson integral Q exponential Q difference polynomial s Quantum calculus Tsallis entropy References Victor Kac, Pokman Cheung, Quantum Calculus ... arxiv.org abs math 9908140 A note on the q derivative operator , 1999 ArXiv math 9908140 Thomas ... more details
Encyclopedia
top
