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.
'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' and 'sich ableiten von' can both say where something comes from or where its origin lies. 'stammen' is more general and sounds very natural with people, things, texts, ideas, or time periods. For example, you say that someone comes from a city or that a quote comes from an author. 'sich ableiten von' often sounds a bit more explanatory and is used especially when you want to show which word, idea, or origin something developed from. In short: 'stammen' names the origin; 'sich ableiten von' tends to explain the path from the origin to the present form.
Der Name der Straße leitet sich von einer alten Mühle ab.
The name of the street is derived from an old mill.
Meine Kollegin stammt aus Bremen, lebt aber seit Jahren in München.
My colleague comes from Bremen but has lived in Munich for years.