derivative

中文： 衍生物、衍生品、衍生产品、衍生工具

1. Something derived.
2. A word formed by derivation, such as stylish from style.
3. A financial instrument whose value depends on the valuation of an underlying asset; such as a warrant, an option etc.
4. A chemical derived from another.
5. The derived function of f(x): the function giving the instantaneous rate of change of f; equivalently, the function giving the slope of the line tangent to the graph of f. Written f'(x) or (df)/(dx) in Leibniz's notation, ̇f(x) in Newton's notation (the latter used particularly when the independent variable is time). · The derivative of x² is 2x; if f(x)#61;x², then f'(x)#61;2x
6. The value of such a derived function for a given value of its independent variable: the rate of change of a function at a point in its domain. · The derivative of f(x)#61;x³ at x#61;2 is 12.
7. Any of several related generalizations of the derivative: the directional derivative, partial derivative, Fréchet derivative, functional derivative, etc.
8. The linear operator that maps functions to their derived functions, usually written D; the simplest differential operator.

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