derivation
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derivation
The logical, step-by-step derivation of a formula, theorem, or conclusion from existing assumptions or principles. This process makes it understandable how a result comes about and is often used in mathematics, logic, and the natural sciences.
Der Professor erklärte die Herleitung der physikalischen Formel an der Tafel.
The professor explained the derivation of the physical formula on the board.
derivation / etymology
The explanation of the origin and historical development of a word; the etymology.
Die Herleitung des Wortes 'Fenster' aus dem Lateinischen ist sehr interessant.
The derivation of the word 'Fenster' (window) from Latin is very interesting.
'Herleitung' (derivation) is the nominalization of the verb 'herleiten' (to derive). This separable verb consists of 'her' (movement from a place toward the speaker) and 'leiten' (to lead). The basic idea is therefore to logically 'lead something out' from an origin, or derive it.
Kannst du mir herleiten, wie du zu diesem Ergebnis gekommen bist?
Can you derive for me how you arrived at this result?
You can recognize the meaning from the context. If it is about formulas, proofs, mathematics, or logic, it means scientific derivation. If it is about words, names, or language, it means the historical linguistic origin (etymology).
Die Herleitung dieser physikalischen Theorie ist sehr komplex.
The derivation of this physical theory is very complex.
To indicate the origin of the derivation, the preposition 'aus' (from) is almost always used with the dative, less commonly 'von' (from/of). The structure is: die Herleitung von etwas aus etwas (the derivation of something from something).
Die Herleitung des Ergebnisses aus den ursprünglichen Daten war fehlerhaft.
The derivation of the result from the original data was flawed.
In a scientific context, 'Herleitung' (derivation) is often combined with verbs such as 'nachvollziehen' (to follow/understand), 'verstehen' (to understand), or 'zeigen' (to show). Typical adjectives are 'logisch' (logical), 'mathematisch' (mathematical), or 'formal' (formal).
Ich kann die logische Herleitung dieses Beweises nicht ganz nachvollziehen.
I can't quite follow the logical derivation of this proof.
origin
For words, Herkunft refers to their etymological origin. Herleitung goes further by explaining how a word developed historically and how its present form or meaning came about. Use Herkunft when simply stating the origin, and Herleitung when explaining the path of development.
Das Wörterbuch erklärt die Herleitung des Wortes vom Lateinischen bis zu seiner heutigen Form.
The dictionary explains the word’s derivation from Latin to its present form.
Das Wörterbuch nennt die lateinische Herkunft des Wortes.
The dictionary gives the Latin origin of the word.
