derivative / drainage / derivation
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derivative
In mathematics, the local rate of change of a function; a central concept in differential calculus.
Im Matheunterricht lernen wir gerade, wie man die Ableitung einer Funktion bildet.
In math class, we are currently learning how to find the derivative of a function.
drainage / diversion
The redirecting or removal of something, especially liquids, gases, or electric current.
Die Ableitung des Regenwassers schützt das Haus vor Feuchtigkeitsschäden.
The drainage of rainwater protects the house from moisture damage.
derivation
In linguistics, the formation of a new word from an existing word stem, often by adding prefixes or suffixes.
Das Wort „fahrbar“ ist eine Ableitung des Verbs „fahren“.
The word 'fahrbar' (driveable) is a derivation of the verb 'fahren' (to drive/go).
deduction / derivation
The logical process by which a conclusion or result is obtained from given information or assumptions.
Seine Schlussfolgerung war eine logische Ableitung aus den Fakten.
His conclusion was a logical deduction from the facts.
'Die Ableitung' (the derivation/derivative) is the noun corresponding to the verb 'ableiten' (to derive/divert). The ending '-ung' is a typical way to form a noun from a verb in German. The basic idea of 'ableiten' (to take something from somewhere else or lead it away) appears in all its meanings.
Man kann viele Adjektive von Verben ableiten.
Many adjectives can be derived from verbs.
You can almost always recognize the meaning of 'Ableitung' (derivation/derivative/drainage) from the context. Words like 'Funktion' (function) or 'berechnen' (to calculate) point to mathematics. 'Wortstamm' (word stem) or 'Silbe' (syllable) point to linguistics, and 'Rohr' (pipe) or 'Wasser' (water) to the technical field.
Die Ableitung des Wortes „glücklich“ ist nicht ganz einfach zu erklären.
The derivation of the word 'glücklich' (happy) is not very easy to explain.
In a mathematical context, 'Ableitung' (derivative) is often used with the verbs 'bilden' (to form/find), 'berechnen' (to calculate), or 'bestimmen' (to determine).
Können Sie die Ableitung dieser komplizierten Funktion bilden?
Can you find the derivative of this complicated function?
In the technical meaning, it usually refers to the removal of liquids. Typical combinations are 'die Ableitung von Regenwasser' (the drainage of rainwater) or 'die Ableitung von Abwasser' (the drainage/removal of wastewater).
Ein verstopftes Rohr behinderte die Ableitung des Schmutzwassers.
A clogged pipe obstructed the drainage of the wastewater.
derivative
In linguistics, both words can relate to a new word formed from an existing word. Die Ableitung (derivation) primarily refers to the formation process, whereas a Derivat is the resulting derived word. Use Ableitung when talking about the formation and Derivat when referring to the result.
Die Ableitung des Wortes „Unfreundlichkeit“ zeigt, wie es aus „freundlich“ gebildet wurde.
The derivation of the word “Unfreundlichkeit” shows how it was formed from “freundlich”.
Das Wort „Unfreundlichkeit“ ist ein Derivat des Adjektivs „freundlich“.
The word “Unfreundlichkeit” is a derivative of the adjective “freundlich”.
