to derive
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to derive
To develop or prove something (a formula, a rule, a conclusion) through logical thinking or a step-by-step derivation from something else.
Im Physikunterricht haben wir gelernt, wie man das Fallgesetz aus einfachen Prinzipien herleitet.
In physics class, we learned how to derive the law of falling bodies from simple principles.
'Herleiten' (to derive) is a separable verb. The prefix 'her-' goes to the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Der Professor leitet die Formel an der Tafel her.
The professor derives the formula on the board.
This verb has two main patterns: you can actively use 'etwas aus etwas herleiten' (to derive something from something) (meaning 1), or it describes an origin with 'etwas leitet sich von etwas her' (something derives from something) (meaning 2). Pay attention to the prepositions 'aus' and 'von' and the reflexive pronoun 'sich'.
Man kann die Lösung aus den gegebenen Informationen herleiten.
One can derive the solution from the given information.
In the meaning 'ableiten' (to derive), 'herleiten' (to derive) is almost always used in a logical, scientific, or mathematical context. It is about proving a conclusion, rule, or formula step by step.
Können Sie herleiten, warum dieses Ergebnis korrekt ist?
Can you derive why this result is correct?
When it is about the origin of words, names, or customs, the reflexive construction 'sich herleiten von' (to derive from) + dative is always used. The subject is the thing whose origin is being described.
Dieser Brauch leitet sich von einem heidnischen Ritual her.
This custom derives from a pagan ritual.
to originate
'stammen' and 'sich herleiten von' can both say where something comes from or what it developed from. 'stammen' is more direct and is often used for origin from a place, a time, or a source. 'sich herleiten von' sounds more formal and fits especially well with words, terms, rules, or developments. The words can be confused because both can name an origin. But the important point is: 'herleiten' without 'sich' often means that you explain something logically or prove it step by step. For simple origin, you usually say 'stammen aus' or 'stammen von'.
Der Name der Stadt leitet sich von einem alten Flussnamen her.
The name of the city derives from an old river name.
Die Familie stammt aus einem kleinen Dorf in der Nähe von Köln.
The family comes from a small village near Cologne.