| 单词 | derivative |
| 释义 | derivative I The rate at which the value of a function increases as its argument increases at any point, if this is defined. In a graph, the first derivative of a function is its slope. If y = f(x), its first derivative at a point x0 is the limit to which [f(x0 + a) - f(x0)]/a tends as a becomes indefinitely small. The first derivative can be written as f′(x), fx, dy/dx or y′(x). The second derivative is defined as the first derivative of the first derivative, and so on. If a function has several arguments, its partial derivatives are its derivatives with respect to one argument, holding the other argument constant; thus if y = f(x, z), ∂y/∂x is the derivative of y as x increases, holding z constant, and ∂y/∂z is the derivative of y with respect to z, holding x constant. See also: cross-partial derivative, first derivative, partial derivative, and second derivative II financial A tradable security whose value is derived from the actual or expected price of some underlying asset, which may be a commodity, a security or a currency. Derivatives include futures contracts, futures on stock market indices, London International Financial Futures and Options Exchange and swaps. Derivatives can be used as a hedge, to reduce risk, or for speculation. A derivatives market is a market such as the London International Financial Futures and Options Exchange (LIFFE) on which derivatives are traded. |
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