Derivative Meaning and Definition
Derivative
Pronunciation
/ˈdɛriˌtɪv/
Part of Speech
Noun
Definition
A mathematical concept representing the rate of change of a function with respect to one of its variables.
Examples
- The derivative of x^2 is 2x.
- finding the derivative of a function is crucial in calculus.
Synonyms
- Rate of Change
- Slope
Antonyms
- Integral
- Constant
Etymology
The word “derivative” comes from the Latin “derivare”, meaning “to take away” or “to derive”. In mathematics, the concept of derivatives emerged in the 17th century, building upon the work of mathematicians such as Sir Isaac Newton and Gottfried Wilhelm Leibniz.
Usage Notes
In mathematical contexts, the word “derivative” is used to describe a specific concept. However, in everyday language, the term can be used more loosely to describe something that is derived or obtained from something else.
Cultural References
The concept of derivatives has appeared in various forms of media, including films, literature, and music. For example, in the novel “A Beautiful Mind”, the character John Nash uses derivatives to solve a mathematical problem.
Idiomatic Expressions or Phrases
- “Derivative work” refers to a work that is created from another work, such as a movie or book.
Related Words or Phrases
- Slope
- Rate of Change
- Integral
Collocations
- “Derivative of a function”
- “Finding the derivative”
Frequency of Use
The word “derivative” is commonly used in academic and professional contexts, particularly in mathematics, science, and engineering. However, it is less commonly used in everyday conversation.
Common Misspellings
- Derivatie
- Derivitive