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noun

die Herleitung, -en

derivation

Definition & meaning

Herleitung means derivation, deduction, or the process of arriving at something from an origin, rule, or chain of reasoning.

It is used in several contexts:

  1. Logical or mathematical derivation
    The step-by-step explanation of how a result, formula, or conclusion is obtained.

    • Die Herleitung der Formel ist kompliziert.
      “The derivation of the formula is complicated.”

  2. Linguistic or etymological derivation
    The explanation of how a word developed from another word or language.

    • Die Herleitung dieses Wortes ist nicht eindeutig.
      “The derivation of this word is not clear.”

  3. General deduction or inference
    The process of reaching a conclusion from evidence or previous information.

    • Die Herleitung seiner Schlussfolgerung überzeugt mich nicht.
      “The reasoning behind his conclusion does not convince me.”

Grammar & Word origin

  • Gender: feminine
  • Article: die
  • Plural: die Herleitungen

The noun comes from the verb herleiten , meaning “to derive,” “to deduce,” or “to infer.”

The verb consists of:

  • her- — indicating movement or derivation toward the speaker’s point of reference
  • leiten — “to lead” or “to guide”

Literally, Herleitung can therefore be understood as “leading something out or toward a result.” Its meaning is closely related to ableiten , “to derive” or “to deduce.”

Synonyms & antonyms

Synonyms

  • Ableitung — “derivation”; very common in mathematics, linguistics, and logic. In mathematics, it can specifically mean a derivative, whereas Herleitung emphasizes the process of explaining how something is obtained.
  • Deduktion — “deduction”; more formal and logical, referring to deriving a conclusion from general principles.
  • Begründung — “justification” or “reasoning”; focuses more on why a claim is valid than on the step-by-step derivation itself.
  • Ableitungsschritt — “derivation step”; refers to one individual step within a derivation.

Antonyms

There is no exact antonym for Herleitung. Depending on the context, possible contrasts include:

  • Annahme — “assumption”; something accepted without being derived or proven.
  • Behauptung — “assertion” or “claim”; a statement presented without necessarily giving a derivation or justification.
  • Intuition — “intuition”; an immediate understanding that does not result from a systematic derivation.

Common phrases & collocations

  • die Herleitung einer Formel — the derivation of a formula
  • die mathematische Herleitung — the mathematical derivation
  • eine Herleitung erklären — to explain a derivation
  • eine Herleitung nachvollziehen — to follow or understand a derivation
  • die etymologische Herleitung — the etymological derivation
  • eine Herleitung aus etwas — a derivation from something
  • eine schlüssige Herleitung — a coherent or convincing derivation

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Examples

Die Herleitung ist einfach.noun

The derivation is simple.

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