derivation

Noun

derivation (countable and uncountable, plural derivations)

1. A leading or drawing off of water from a stream or source.
2. The act of receiving anything from a source; the act of procuring an effect from a cause, means, or condition, as profits from capital, conclusions or opinions from evidence.
3. (genealogy) The act of tracing origin or descent; an instance thereof (for example, an etymology).
   • the derivation of a word from an Indo-European root
4. Forming a new word by changing the base of another word or by adding affixes to it.
5. The state or method of being derived; the relation of origin when established or asserted.
6. That from which a thing is derived.
7. That which is derived; a derivative; the result of a deduction.
   • There were also letters to scientists and other scholars, pages of derivations of mathematics and physics formulae, and copious writings on alchemy and religion.2014 June 21, “Magician’s brain”, in The Economist, volume 411, number 8892, archived from the original on 09 Jan 2025
8. The process of deriving one thing from another, especially in logic; a deduction.
   1. A formal proof: a sequence of statements, each of which is logically entailed by those preceding (with respect to some collection of rules of inference), the initial statements being taken as axioms.
9. The process of application of the derivative operator to a function, yielding another function called the derived function of the first.
10. (differential algebra) An algebraic generalization of the derivative operator (from its natural setting in the ring of real-valued functions) to a general associative algebra over a field. Formally, (given an algebra A over a field K) a K-linear endomorphism that satisfies Leibnitz's Law.
    1. (differential algebra) Any of several generalizations of this notion: a Hasse–Schmidt derivation, a graded derivation, etc.
11. (historical) A drawing of humors or fluids from one part of the body to another, to relieve or lessen a morbid process.