Derivative

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). 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 is advanced.

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.

Derivative (finance)

In finance, a derivative is a contract that derives its value from the performance of an underlying entity. This underlying entity can be an asset, index, or interest rate, and often called the "underlying". Derivatives can be used for a number of purposes, including insuring against price movements (hedging), increasing exposure to price movements for speculation or getting access to otherwise hard-to-trade assets or markets. Some of the more common derivatives include forwards, futures, options, swaps, and variations of these such as synthetic collateralized debt obligations and credit default swaps. Most derivatives are traded over-the-counter (off-exchange) or on an exchange such as the Bombay Stock Exchange, while most insurance contracts have developed into a separate industry. Derivatives are one of the three main categories of financial instruments, the other two being stocks (i.e., equities or shares) and debt (i.e., bonds and mortgages).

Collateralized debt obligation

Derivative (chemistry)

In chemistry, a derivative is a compound that is derived from a similar compound by a chemical reaction.

In the past, derivative also meant a compound that can be imagined to arise from another compound, if one atom or group of atoms is replaced with another atom or group of atoms, but modern chemical language now uses the term structural analog for this meaning, thus eliminating ambiguity. The term "structural analogue" is common in organic chemistry.

In biochemistry, the word is used for compounds that at least theoretically can be formed from the precursor compound.

Chemical derivatives may be used to facilitate analysis. For example, melting point (MP) analysis can assist in identification of many organic compounds. A crystalline derivative may be prepared, such as a semicarbazone or 2,4-dinitrophenylhydrazone (derived from aldehydes or ketones), as a simple way of verifying the identity of the original compound, assuming that a table of derivative MP values is available. Prior to the advent of spectroscopic analysis, such methods were widely used.

Credit

Credit may refer to:

See also

Debits and credits

In double entry bookkeeping, debits and credits (abbreviated Dr and Cr, respectively) are entries made in account ledgers to record changes in value resulting from business transactions. Generally speaking, the source account for the transaction is credited (that is, an entry is made on the right side of the account's ledger) and the destination account is debited (that is, an entry is made on the left side). Total debits must equal total credits for each transaction; individual transactions may require multiple debit and credit entries to record.

The difference between the total debits and total credits in a single account is the account's balance. If debits exceed credits, the account has a debit balance; if credits exceed debits, the account has a credit balance. For the company as a whole, the totals of debit balances and credit balances must be equal as shown in the trial balance report, otherwise an error has occurred.

Accountants use the trial balance to prepare financial statements (such as the balance sheet and income statement) which communicate information about the company's financial activities in a generally accepted standard format.

Credit (finance)

Credit (from Latin credit, "(he/she/it) believes") is the trust which allows one party to provide money or resources to another party where that second party does not reimburse the first party immediately (thereby generating a debt), but instead arranges either to repay or return those resources (or other materials of equal value) at a later date. The resources provided may be financial (e.g. granting a loan), or they may consist of goods or services (e.g. consumer credit). Credit encompasses any form of deferred payment. Credit is extended by a creditor, also known as a lender, to a debtor, also known as a borrower.

Credit does not necessarily require money. The credit concept can be applied in barter economies as well, based on the direct exchange of goods and services. However, in modern societies, credit is usually denominated by a unit of account. Unlike money, credit itself cannot act as a unit of account.

Movements of financial capital are normally dependent on either credit or equity transfers. Credit is in turn dependent on the reputation or creditworthiness of the entity which takes responsibility for the funds. Credit is also traded in financial markets. The purest form is the credit default swap market, which is essentially a traded market in credit insurance. A credit default swap represents the price at which two parties exchange this risk – the protection seller takes the risk of default of the credit in return for a payment, commonly denoted in basis points (one basis point is 1/100 of a percent) of the notional amount to be referenced, while the protection buyer pays this premium and in the case of default of the underlying (a loan, bond or other receivable), delivers this receivable to the protection seller and receives from the seller the par amount (that is, is made whole).