derivative

abgeleitet, unoriginell

Aus etwas anderem übernommen oder entwickelt, statt neu oder eigenständig zu sein.

In einfachem Englisch: Taken or developed from something else, rather than being new or original.

• The film feels derivative.
• Her early paintings were derivative of older artists' work.
• Critics called the novel entertaining but highly derivative.

So benutzt man es: derivative of something (His style is derivative of earlier crime writers.)

Synonyme: unoriginal, imitative, derived

Gegenteile: original

Häufige Wendungen: derivative work, derivative style, highly derivative

Derivat

Etwas, das aus etwas anderem hergestellt wird, besonders ein Stoff, der durch Veränderung eines anderen chemischen Stoffs entsteht.

In einfachem Englisch: Something made from another thing, especially a chemical made by changing another chemical.

• This compound is a sugar derivative.
• The laboratory tested three derivatives of the original substance.
• Some oil derivatives are used to make plastics.

So benutzt man es: a derivative of something (This medicine contains a derivative of a natural plant chemical.)

Synonyme: derived product

Häufige Wendungen: a chemical derivative, a derivative of something, an oil derivative

Ableitung

Mathematische Funktion, die angibt, wie schnell sich eine andere Funktion an jedem Punkt verändert.

In einfachem Englisch: A mathematical function that shows how fast another function changes at each point.

• Find the derivative of this function.
• The derivative describes how quickly the curve rises or falls.
• We calculated first and second derivatives in class.

So benutzt man es: the derivative of a function (The derivative of this function is constant.); derivative with respect to a variable (Find the derivative with respect to time.)

Synonyme: derived function

Häufige Wendungen: first derivative, calculate the derivative, derivative of something

Ableitung, Ableitungswert

Zahl, die angibt, wie schnell sich eine mathematische Funktion an einem bestimmten Punkt verändert.

In einfachem Englisch: The number showing how fast a mathematical function changes at one particular point.

• The derivative here is positive.
• At the highest point, the derivative equals zero.
• What is the derivative of this function at three?

So benutzt man es: the derivative at + point (The derivative at this point is zero.)

Synonyme: instantaneous rate of change

Häufige Wendungen: derivative at zero, a positive derivative, a negative derivative