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1. Dictionary

   derivation

   /ˌdɛrɪˈveɪʃn/

   noun

   • 1. the action of obtaining something from a source or origin: "the derivation of scientific laws from observation" Similar derivinginductiondeductiondeducinginferringinferencegatheringgleaningdrawing outextractionelicitingrare:eduction
   • ▪ the formation of a word from another word or from a root in the same or another language. Similar originetymologysourcerootetymonprovenancefountainheadwellspringoriginationbeginningfoundationbasiscauseancestrydescentgenealogydevelopmentevolutionextraction
   • ▪ origin; extraction: "music of primarily Turkish derivation"
   • ▪ something derived; a derivative: "a good dictionary includes derivations"
   • 2. the set of stages that link a sentence in a natural language to its underlying logical form.
   • 3. the process of deducing a new formula, theorem, etc., from previously accepted statements.
   • ▪ a sequence of statements showing that a formula, theorem, etc., is a consequence of previously accepted statements.

   Word Origin late Middle English (denoting the drawing of a fluid, especially pus or blood; also in the sense ‘formation of a word from another word’): from Latin derivatio(n-), from the verb derivare (see derive).

   Derivatives

   • 1. derivational adjective

   Scrabble Points: 14

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2. math.libretexts.org › Courses › Mount_Royal2.1: Derivative as a Function - Mathematics LibreTexts

   math.libretexts.org › Courses › Mount_Royal

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   Sep 26, 2024 · The derivative function, denoted by f′, is the function whose domain consists of those values of \ (x\) such that the following limit exists: \ [f′ (x)=\displaystyle \displaystyle \lim_ {h→0}\frac {f (x+h)−f (x)} {h}.\] A function \ (f (x)\) is said to be differentiable at a if \ (f' (a)\) exists.

3. Videos

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     23:31

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     Definition of the Derivative

     22 Feb 2018

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     7:16

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     Derivative as a concept | Derivatives introduction | AP Calculus AB | Khan Academy

     19 Jul 2017

     951.3K views

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     58:04

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     Derivatives for Beginners - Basic Introduction

     27 Jul 2020

     1.2M views

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4. math.libretexts.org › Courses › Mount_Royal2.2: Techniques of differentiation - Mathematics LibreTexts

   math.libretexts.org › Courses › Mount_Royal

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   Sep 24, 2024 · By using the continuity of \(g(x)\), the definition of the derivatives of \(f(x)\) and \(g(x)\), and applying the limit laws, we arrive at the product rule, \[j′(x)=f′(x)g(x)+g′(x)f(x).\]

5. www.nagwa.com › en › explainersLesson Explainer: Second- and Higher-Order Derivatives | Nagwa

   www.nagwa.com › en › explainers

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   2 days ago · In this explainer, we will learn how to find second- and higher-order derivatives of a function including using differentiation rules.

6. People also ask

   What is a derivative function?

   • The derivative function gives the derivative of a function at each point in the domain of the original function for which the derivative is defined. We can formally define a derivative function as follows. Let \ (f\) be a function.

   2.1: Derivative as a Function - Mathematics LibreTexts

   math.libretexts.org/Courses/Mount_Royal_University/Calculus_for_Scientists_I/2:_Derivatives/2.1:_Derivative_as_a_Function

   See all results for this question

   What is a derivative of velocity?

   • The derivative of velocity is the rate of change of velocity, which is acceleration. The new function obtained by differentiating the derivative is called the second derivative. Furthermore, we can continue to take derivatives to obtain the third derivative, fourth derivative, and so on.

   2.1: Derivative as a Function - Mathematics LibreTexts

   math.libretexts.org/Courses/Mount_Royal_University/Calculus_for_Scientists_I/2:_Derivatives/2.1:_Derivative_as_a_Function

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   What is a derivative of a position function?

   • For example, the derivative of a position function is the rate of change of position, or velocity. The derivative of velocity is the rate of change of velocity, which is acceleration. The new function obtained by differentiating the derivative is called the second derivative.

   2.1: Derivative as a Function - Mathematics LibreTexts

   math.libretexts.org/Courses/Mount_Royal_University/Calculus_for_Scientists_I/2:_Derivatives/2.1:_Derivative_as_a_Function

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   What is the derivative of the quotient of two functions?

   • The derivative of the quotient of two functions is the derivative of the first function times the second function minus the derivative of the second function times the first function, all divided by the square of the second function.

   2.2: Techniques of differentiation - Mathematics LibreTexts

   math.libretexts.org/Courses/Mount_Royal_University/Calculus_for_Scientists_I/2:_Derivatives/2.2:_Techniques_of_differentiation

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   What is the derivative of the product of two functions?

   • The first one examines the derivative of the product of two functions. Although it might be tempting to assume that the derivative of the product is the product of the derivatives, similar to the sum and difference rules, the product rule does not follow this pattern.

   2.2: Techniques of differentiation - Mathematics LibreTexts

   math.libretexts.org/Courses/Mount_Royal_University/Calculus_for_Scientists_I/2:_Derivatives/2.2:_Techniques_of_differentiation

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   How do you find the derivative of a function?

   • Find values of a and b that make \ (f (x)=\begin {cases}ax+b & if x<3\\x^2 & if x≥3\end {cases}\) both continuous and differentiable at \ (3\). Use Example as a guide. The derivative of a function is itself a function, so we can find the derivative of a derivative.

   2.1: Derivative as a Function - Mathematics LibreTexts

   math.libretexts.org/Courses/Mount_Royal_University/Calculus_for_Scientists_I/2:_Derivatives/2.1:_Derivative_as_a_Function

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7. www.britannica.com › science › mathematicsMathematics - Calculus, Derivatives, Integrals | Britannica

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   4 days ago · By definition, the derivative of A(t) is equal to [A(t + h) − A(t)]/h as h tends to zero. Note that the dark blue-shaded region in the illustration is equal to the numerator of the preceding quotient and that the striped region, whose area is equal to its base h times its height f ( t ), tends to the same value for small h .

8. www.nagwa.com › en › explainersLesson Explainer: Definition of the Derivative | Nagwa

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   Sep 25, 2024 · Definition: Derivative of a Function. The derivative of a function at a point 𝑥 is defined as l i m → 𝑓 (𝑥 + ℎ) − 𝑓 (𝑥) ℎ, where this limit exists. An alternative but equivalent definition of the derivative at 𝑥 is l i m → 𝑓 (𝑥) − 𝑓 (𝑥) 𝑥 − 𝑥, if the limit exists.

9. www.nagwa.com › en › lessonsLesson: Definition of the Derivative - Nagwa

   www.nagwa.com › en › lessons

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   Oct 9, 2024 · In this lesson, we will learn how to calculate the derivative of a function using the formal definition of the derivative as a limit.

10. math.libretexts.org › Bookshelves › Calculus14.5: The Chain Rule for Multivariable Functions

    math.libretexts.org › Bookshelves › Calculus

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    Oct 8, 2024 · Perform implicit differentiation of a function of two or more variables. In single-variable calculus, we found that one of the most useful differentiation rules is the chain rule, which allows us to find the derivative of the composition of two functions.