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Derivative
01
导数
the rate at which a function changes with respect to its independent variable
Example
Finding the derivative of a distance function results in the instantaneous speed function, representing the speed of an object at a specific moment.
The derivative of a revenue function provides the marginal revenue, indicating the additional revenue gained from selling one more unit.
In economics, the elasticity of a demand function is determined by finding the derivative with respect to price.
02
派生词, 衍生词
(in linguistics) a word that is developed from another word or base
What is a "derivative"?
A derivative is a word formed from an existing word by adding an affix or making changes that result in a new meaning or part of speech. This process often involves the addition of prefixes or suffixes to the base or root word. For example, the noun "happy" can be transformed into the adjective "unhappy" by adding the prefix "un-", or into the noun "happiness" by adding the suffix "-ness". Derivatives expand the vocabulary of a language and allow for the expression of different concepts and grammatical categories, enhancing communication by providing various forms and meanings related to a root word.
03
衍生品
a financial contract whose value depends on the price or performance of another asset, such as stocks, bonds, or commodities
04
衍生物, 派生物
a substance that is derived or obtained from another substance
derivative
01
派生的, 模仿的
resembling or imitating a previous work, often in a way that lacks originality
Example
The derivative fashion line lacked creativity, merely replicating trends from previous seasons.
The film was criticized for its derivative plot, which closely resembled that of a popular novel.
His artwork was deemed derivative, as it closely imitated the style of a famous painter.
02
衍生的
(of a product) having a value determined by an underlying asset or variable
例子
Finding the derivative of a distance function results in the instantaneous speed function, representing the speed of an object at a specific moment.
The derivative of a revenue function provides the marginal revenue, indicating the additional revenue gained from selling one more unit.
In economics, the elasticity of a demand function is determined by finding the derivative with respect to price.
Calculating the derivative of a position function yields the velocity function, describing the rate of change of position with respect to time.
The chain rule allows finding the derivative of composite functions, crucial for analyzing complex mathematical expressions.
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