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Derivative
01
производная
the rate at which a function changes with respect to its independent variable, representing the slope of the tangent line to the function's graph
02
производное слово
(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.
04
производное
a compound obtained from, or regarded as derived from, another compound
derivative
01
производный
formed from an idea that is a slight or full copy of something else
Пример
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.
