Category: Derivative


The derivative of a function of a real variable measures the sensitivity to change of the function value output value with respect to a change in its argument input value. Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity : this measures how quickly the position of the object changes when time advances. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point.

The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the "instantaneous rate of change", the ratio of the instantaneous change in the dependent variable to that of the independent variable. Derivatives may be generalized to functions of several real variables. In this generalization, the derivative is reinterpreted as a linear transformation whose graph is after an appropriate translation the best linear approximation to the graph of the original function.

The Jacobian matrix is the matrix that represents this linear transformation with respect to the basis given by the choice of independent and dependent variables.

It can be calculated in terms of the partial derivatives with respect to the independent variables. For a real-valued function of several variables, the Jacobian matrix reduces to the gradient vector.

The process of finding a derivative is called differentiation. The reverse process is called antidifferentiation. The fundamental theorem of calculus relates antidifferentiation with integration.

Differentiation and integration constitute the two fundamental operations in single-variable calculus. Differentiation is the action of computing a derivative. It is called the derivative of f with respect to x.

If x and y are real numbersand if the graph of f is plotted against xthe derivative is the slope of this graph at each point. The simplest case, apart from the trivial case of a constant functionis when y is a linear function of xmeaning that the graph of y is a line.

The above formula holds because. If the function f is not linear i. Two distinct notations are commonly used for the derivative, one deriving from Gottfried Wilhelm Leibniz and the other from Joseph Louis Lagrange. A third notation, first used by Isaac Newtonis sometimes seen in physics.

In Leibniz's notationan infinitesimal change in x is denoted by dxand the derivative of y with respect to x is written. The above expression is read as "the derivative of y with respect to x ", " dy by dx ", or " dy over dx ".

The oral form " dy dx " is often used conversationally, although it may lead to confusion.


Lagrange's notation is sometimes incorrectly attributed to Newton. Newton's notation for differentiation also called the dot notation for differentiation places a dot over the dependent variable. That is, if y is a function of tthen the derivative of y with respect to t is. Newton's notation is generally used when the independent variable denotes time.

The most common approach to turn this intuitive idea into a precise definition is to define the derivative as a limit of difference quotients of real numbers. Let f be a real valued function defined in an open neighborhood of a real number a. In classical geometry, the tangent line to the graph of the function f at a was the unique line through the point af a that did not meet the graph of f transversallymeaning that the line did not pass straight through the graph. The derivative of y with respect to x at a is, geometrically, the slope of the tangent line to the graph of f at af a.

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These lines are called secant lines. A value of h close to zero gives a good approximation to the slope of the tangent line, and smaller values in absolute value of h will, in general, give better approximations.A derivative is a contract between two or more parties whose value is based on an agreed-upon underlying financial asset like a security or set of assets like an index. Common underlying instruments include bonds, commodities, currencies, interest rates, market indexes, and stocks.

Derivatives are secondary securities whose value is solely based derived on the value of the primary security that they are linked to—called the underlying. Typically, derivatives are considered advanced investing. There are two classes of derivative products—"lock" and " option.

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Option products e. While a derivative's value is based on an asset, ownership of a derivative doesn't mean ownership of the asset.

Futures contracts, forward contracts, options, swapsand warrants are commonly used derivatives. A futures contractfor example, is a derivative because its value is affected by the performance of the underlying asset. A futures contract is a contract to buy or sell a commodity or security at a predetermined price and at a preset date in the future. Futures contracts are standardized for by specific quantity sizes and expirations dates.


Futures contracts can be used with commodities, such as oil and wheat, and precious metals such as gold and silver. An equity or stock option is a type of derivative because its value is "derived" from that of the underlying stock. Options come in forms: calls and puts. A call option gives the holder the right to buy the underlying stock at a preset price called the strike price and by a predetermined date outlined in the contract called the expiration date.

A put option gives the holder the right to sell the stock at the preset price and date outlined in the contract. There's an upfront cost to an option called the option premium. The risk-reward equation is often thought to be the basis for investment philosophy and derivatives can be used to either mitigate risk hedgingor they can be used for speculation where the level of risk versus reward would be considered.

Derivatives used as a hedge allow the risks associated with the underlying asset's price to be transferred between the parties involved in the contract. Some derivatives are traded on national securities exchanges and are regulated by the U. Other derivatives are traded over-the-counter OTCwhich involve individually negotiated agreements between parties. Most derivatives are traded on exchanges.

The CFTC regulates the futures markets and is a federal agency that is charged with regulating the markets so that the markets function in a fair manner. The oversight can include preventing fraud, abusive trading practices, and regulating brokerage firms.

The members of these exchanges are regulated by the SEC, which monitors the markets to ensure they are functioning properly and fairly. It's important to note that regulations can vary somewhat, depending on the product and its exchange.

In the currency market, for example, the trades are done via over-the-counter OTCwhich is between brokers and banks versus a formal exchange. Two parties, such as a corporation and a bank, might agree to exchange a currency for another at a specific rate in the future.

Banks and brokers are regulated by the SEC.Derivativein mathematicsthe rate of change of a function with respect to a variable. Derivatives are fundamental to the solution of problems in calculus and differential equations.

Derivative Tricks (That Teachers Probably Don't Tell You)

In general, scientists observe changing systems dynamical systems to obtain the rate of change of some variable of interestincorporate this information into some differential equationand use integration techniques to obtain a function that can be used to predict the behaviour of the original system under diverse conditions. Geometrically, the derivative of a function can be interpreted as the slope of the graph of the function or, more precisely, as the slope of the tangent line at a point.

Its calculation, in fact, derives from the slope formula for a straight line, except that a limiting process must be used for curves.

This change in notation is useful for advancing from the idea of the slope of a line to the more general concept of the derivative of a function. For a curve, this ratio depends on where the points are chosen, reflecting the fact that curves do not have a constant slope. To find the slope at a desired point, the choice of the second point needed to calculate the ratio represents a difficulty because, in general, the ratio will represent only an average slope between the points, rather than the actual slope at either point see figure.

To get around this difficulty, a limiting process is used whereby the second point is not fixed but specified by a variable, as h in the ratio for the straight line above. Finding the limit in this case is a process of finding a number that the ratio approaches as h approaches 0, so that the limiting ratio will represent the actual slope at the given point. Consider, for example, the parabola given by x 2. Differentiation —i. Article Media.

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Learn More in these related Britannica articles:. The second derivative often has a useful physical interpretation. For example, if…. The time taken is h.

Therefore, the average speed over that time interval….A derivative is a financial security with a value that is reliant upon or derived from, an underlying asset or group of assets—a benchmark.

The derivative itself is a contract between two or more parties, and the derivative derives its price from fluctuations in the underlying asset. The most common underlying assets for derivatives are stocks, bonds, commodities, currencies, interest rates, and market indexes.

These assets are commonly purchased through brokerages. See how your broker compares with Investopedia list of the best online brokers. Derivatives can trade over-the-counter OTC or on an exchange. OTC derivatives constitute a greater proportion of the derivatives market. OTC-traded derivatives, generally have a greater possibility of counterparty risk.

Counterparty risk is the danger that one of the parties involved in the transaction might default. These parties trade between two private parties and are unregulated. Conversely, derivatives that are exchange-traded are standardized and more heavily regulated.

Derivatives can be used to hedge a position, speculate on the directional movement of an underlying asset, or give leverage to holdings. Their value comes from the fluctuations of the values of the underlying asset.


Originally, derivatives were used to ensure balanced exchange rates for goods traded internationally. With the differing values of national currencies, international traders needed a system to account for differences. Today, derivatives are based upon a wide variety of transactions and have many more uses. There are even derivatives based on weather data, such as the amount of rain or the number of sunny days in a region.

For example, imagine a European investor, whose investment accounts are all denominated in euros EUR. This investor purchases shares of a U. Now the investor is exposed to exchange-rate risk while holding that stock. Exchange-rate risk the threat that the value of the euro will increase in relation to the USD.Entry 1 of 2 1 linguistics : a word formed from another word or base : a word formed by derivation "pointy," "pointed," and other derivatives of "point" 2 : something derived … the sonata form itself a derivative of opera … — Kingsley Martin the name "Mia" is a derivative of "Maria" 3 mathematics : the limit of the ratio of the change in a function to the corresponding change in its independent variable as the latter change approaches zero 4 chemistry a : a chemical substance related structurally to another substance and theoretically derivable from it b : a substance that can be made from another substance Petroleum is a derivative of coal tar.

Petroleum is a derivative of coal tar. Adjective A number of critics found the film derivative and predictable. His style seems too derivative of Hemingway. Williamson, National Review"Apocalypse Now? Does it actually work?


Send us feedback. See More First Known Use of derivative Noun 15th century, in the meaning defined at sense 1 Adjective circain the meaning defined at sense 1 History and Etymology for derivative Noun see derive Adjective see derive Keep scrolling for more Learn More about derivative Share derivative Post the Definition of derivative to Facebook Share the Definition of derivative on Twitter Time Traveler for derivative.

See more words from the same century Dictionary Entries near derivative derivate derivation derivationist derivative derivative citizenship derivative deposit derivative hybrid. Accessed 12 Oct. Keep scrolling for more More Definitions for derivative derivative. Entry 1 of 2 : a word formed from another word : something that comes from something else : a substance that is made from another substance derivative.

Entry 1 of 2 1 : formed by derivation 2 : made up of or marked by derived elements derivative. Entry 1 of 2 : a contract or security that derives its value from that of an underlying asset as another security or from the value of a rate as of interest or currency exchange or index of asset value as a stock index Note: Derivatives often take the form of customized contracts transacted outside of security exchanges, while other contracts, such as standard index options and futures, are openly traded on such exchanges.

Derivatives often involve a forward contract. Please tell us where you read or heard it including the quote, if possible. Test Your Vocabulary Forms of Government Quiz A gerontocracy is rule by: soothsayers unwritten laws animals elders Can you spell these 10 commonly misspelled words? Test Your Knowledge - and learn some interesting things along the way.

Subscribe to America's largest dictionary and get thousands more definitions and advanced search—ad free! Convening on 'Counsel' and 'Council' We drop the gavel. Ask the Editors 'Intensive purposes': An Eggcorn We're intent on clearing it up 'Nip it in the butt': An Eggcorn We're gonna stop you right there Literally How to use a word that literally drives some pe Is Singular 'They' a Better Choice?

Or something like that. A challenging quiz of changing words. Can you spell these 10 commonly misspelled words? Listen to the words and spell through all three l Login or Register. Save Word. Keep scrolling for more. Other Words from derivative Adjective derivatively adverb.Simply add the final score of each team.

Odds and the number of teams vary from casino to casino. The following are approximate odds:Any game that results in a push reduces the parlay one team.

A two-team parlay would become a straight bet. This increases the probability of winning your bet but decreases the odds of the parlay. Odds and the number of points available to "tease" vary from casino to casino. The following are approximate odds:To bet on boxing, tell the ticket writer the bet number of the boxer you wish to bet and the amount you wish to wager. Boxing odds are shown using a "Money Line. A "minus" (-) preceding the number indicates a favorite.

Tyson is favored to win the bout. Boxing matches often feature money line proposition wagers on knockouts, draws, rounds and the duration of the fight. Odds vary on each fight. To bet on football, tell the ticket writer the bet number of the team you wish to bet, with the point spread and the amount you wish to wager.

The point spread: When betting on football, the team you bet on must "cover the spread. If you bet the Dolphins, the Dolphins must win by 7 points for you to win your bet. If you bet the Jets, any of the following will declare you a winner. The listed point spread at the time you make your bet may be different from the point spread when the game starts.

In some cases, bettors have the option to discard the point spread and bet on which team will win. You may combine several teams into one wager. Sports books offer a number of different cards, each one having different rules. Rules for parlay cards are placed on the back of each card.

Read them carefully before wagering.

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The cards are simple to fill out. Simply darken the boxes, or circles, that apply to the teams you wish to parlay. Then darken the amount you want to bet. The following are approximate odds:Sports books offer bettors the opportunity to wager on the outcome of a season -- for example, which team will win the Super Bowl or the Stanley Cup or the American League East pennant.

This is known as "futures book" or "future book" betting. As an illustration, let's look at Super Bowl futures. Sports books list each NFL team with corresponding odds to win the Super Bowl. For example, the Ravens may be 5-1, the Redskins 12-1, the Cardinals 100-1, etc. It does not matter whether your team covers the point spread in the Super Bowl.

For the purposes of future book betting, the team has to win only the Super Bowl. When you make a futures bet, your odds are "locked in. Futures betting also is offered on the major events in horse racing, such as the Kentucky Derby and Breeders' Cup.

In horse racing futures, if your horse does not start the race due to injury or any other reason, you lose the bet -- there are no refunds. On the other hand, the odds on your horse racing futures bet also are "locked in," regardless of the horse's odds on race day. Some sports books offer futures betting on unusual propositions, such as which major league baseball player will hit the most home runs in the regular season.

Note that in this type of wager, all bets are action regardless of injuries or other unforeseen events. This type of wager is typically found on pro football and major league baseball, and sometimes on pro basketball.Did this article help you.

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Yes No Cookies make wikiHow better. By continuing to use our site, you agree to our cookie policy. Co-authors: 9 Michael Milligan Oct 19 "Although I don't bet for religious reasons, I wanted to understand the likelihood of an outcome in the eyes of those who have real money on the line. FYI, the stars don't appear to stay selected when I click on them, but I tried to give five stars.

I've tried learning this before, but it's always very confusing. This helped me make sense of it. Jul 23 "I was reading about the McGregor-Mayweather fight, so I wanted to understand all the talk surrounding the betting. This cleared up nearly all of my questions. Helped me fit into the conversation that was partaking behind me.

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To convert decimal odds to fractional, subtract 1. To convert moneyline odds to decimal, if the moneyline is positive, divide by 100 and add 1. If it is negative, divide 100 by the moneyline amount (without the minus sign) and add 1.

To convert fractional odds to decimal, divide the first figure by the second figure add 1.


Becoming less popular online. Tell you the amount of profit relative to your stake if you win your bets. Decimal Odds (Also known as European) Common around the world but especially in Europe. Standard on betting exchanges such as Betfair. Convey the total amount you will receive if you win, including the return of your stake.

Moneyline Odds (Also known as American) Used by most US bookmakers.

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Betting Calculators and Guides Odds ConverterEach Way CalculatorBack Lay CalculatorBetting TermsTic-Tac GuideCompare Free Bets at BonusBetting Contact - LinksYou can also convert odds in a small pop-up window for easy browsing.

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