derived function
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Definition
- Noun:
- The result of mathematical differentiation: In calculus, the "derived function" is the function obtained by differentiating another function. It represents the rate at which the original function's value changes.
- The instantaneous rate of change: It measures how one quantity changes instantaneously relative to a change in another quantity, often expressed as df(x)/dx or f'(x).
Usage Examples
- Noun:
- To find the slope of the curve at any point, you must calculate the derived function.
- The derived function of position with respect to time is velocity.
Advanced Usage
- Fundamental Concept in Calculus: The derived function is central to differential calculus, used for finding tangents, optimizing functions, and modeling rates of change in physics, economics, and engineering.
- Notation: Commonly denoted as f'(x), dy/dx, or df/dx. The process of finding it is called "differentiation."
Variants and Related Words
- Derivative (n): The most common synonym for "derived function." ()
- Differentiation (n): The mathematical operation of finding a derived function.
- Differential Calculus (n): The branch of calculus concerned with derivatives and their applications.
Synonyms
- Derivative
- Differential Coefficient
- Rate-of-change function
Related Phrases
- First derived function: The derivative obtained from the first differentiation.
- Higher-order derived function: A function obtained by differentiating a derived function multiple times (e.g., second derivative f''(x)).
Noun
- the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx