to derive / divert / differentiate
Loading your saved state.
to derive
To logically derive a conclusion or insight from existing information or observations.
Aus seinem Verhalten lässt sich ableiten, dass er mit der Situation unzufrieden ist.
From his behavior, it can be derived that he is unhappy with the situation.
to divert
To deliberately guide something (such as water, electricity, heat) along another path or to another place.
Ein Blitzableiter soll den Blitz sicher in die Erde ableiten.
A lightning rod is meant to safely divert lightning into the ground.
to be derived from
To have its origin in something; to come from something.
Das deutsche Wort 'Fenster' leitet sich vom lateinischen Wort 'fenestra' ab.
The German word 'Fenster' is derived from the Latin word 'fenestra'.
to differentiate
In mathematics, to determine the derivative (the differential quotient) of a function.
Können Sie die Funktion f(x) = x² nach x ableiten?
Can you differentiate the function f(x) = x² with respect to x?
'Ableiten' (to derive / divert / differentiate) is a separable verb. The prefix 'ab-' stands at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Der Detektiv leitet daraus eine wichtige Spur ab.
The detective derives an important clue from it.
The verb consists of the prefix 'ab-' (away from) and the verb 'leiten' (to guide/lead). So the basic idea is to 'guide' something from one point to another—whether it is a logical conclusion, water, or the origin of a word.
Man kann die Regel aus dem Beispiel ableiten.
You can derive the rule from the example.
In the logical meaning, the structure 'etwas (Akkusativ) aus etwas (Dativ) ableiten' (to derive something from something) is used. The preposition 'aus' is crucial here.
Aus diesen Daten können wir keine klaren Schlüsse ableiten.
We cannot derive any clear conclusions from these data.
In technical or physical contexts, 'ableiten' (to divert/conduct away) is often combined with things like 'Wasser' (water), 'Strom' (electricity), 'Wärme' (heat), or 'einen Blitz' (a lightning strike).
Die neue Drainage soll das Regenwasser besser vom Haus ableiten.
The new drainage system is supposed to divert rainwater away from the house more effectively.
When referring to origin, the verb is used reflexively with the preposition 'von': 'sich ableiten von etwas (Dativ)' (to be derived from something).
Viele moderne Bräuche leiten sich von alten Traditionen ab.
Many modern customs are derived from old traditions.
You can recognize the mathematical meaning from the context. If 'Funktion' (function), 'Variable' (variable), or formulas are being discussed, it is about differentiation. The preposition 'nach' is often used.
In der Prüfung mussten wir eine komplexe Funktion nach der Variablen t ableiten.
In the exam, we had to differentiate a complex function with respect to the variable t.
to originate
Stammen generally states the origin of a word or term. Sich ableiten von places greater emphasis on the fact that the present form or meaning developed from an older form. Use stammen for simply stating an origin and sich ableiten when there is a clear derivational or developmental relationship.
Die heutige Bezeichnung leitet sich von einem lateinischen Wort ab.
The current term is derived from a Latin word.
Die Bezeichnung stammt aus dem Lateinischen.
The term originates from Latin.
