derivative

1. Something derived.

   Ableitung

   произво́дноеproizvódnoje

   (linguistics) a word that is derived from another word

2. A word formed by derivation, such as stylish from style.

3. A financial instrument whose value depends on the valuation of an underlying asset; such as a warrant, an option etc.

   Derivat

   деривати́вderivatív

   a financial instrument whose value is based on another security

4. A chemical derived from another.

   Ableitung, Derivation, Derivat

   дерива́тderivát, произво́дное сло́воproizvódnoje slóvo, произво́дноеproizvódnoje

   a compound obtained from, or regarded as derived from, another compound

5. One of the two fundamental objects of study in calculus (the other being integration), which quantifies the rate of change, tangency, and other qualities arising from the local behavior of a function.

   The derived function of f(x): the function giving the instantaneous rate of change of f; equivalently, the function giving the slope of the line tangent to the graph of f. Written f'(x) or (df)/(dx) in Leibniz's notation, ̇f(x) in Newton's notation (the latter used particularly when the independent variable is time).

   The derivative of x² is 2x; if f(x)#61;x², then f'(x)#61;2x

6. The value of such a derived function for a given value of its independent variable: the rate of change of a function at a point in its domain.

   The derivative of f(x)#61;x³ at x#61;2 is 12.

   Ableitung

   произво́днаяproizvódnaja

7. Any of several related generalizations of the derivative: the directional derivative, partial derivative, Fréchet derivative, functional derivative, etc.

8. The linear operator that maps functions to their derived functions, usually written D; the simplest differential operator.

1. What is the derivative of eˣ?

   Яка похідна від e^x?

   deWas ist die Ableitung von e^x?

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2. L'Hôpital's rule uses derivatives to help evaluate limits involving indeterminate forms.

   Правило Лопіталя використовує похідні для розрахунку границь, що містять невизначенності.

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3. This was a translation of copyrighted material, so I deleted it since copyright owners have the right to control derivative works.

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4. Differential equations are equations involving derivatives.

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5. That drug is a derivative of quinine.

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