Keyword Analysis & Research: definition of derivative

lamar.edu

https://tutorial.math.lamar.edu/classes/calcI/DefnOfDerivative.aspx

Note that we replaced all the a’s in (1)(1) with x’s to acknowledge the fact that the derivative is really a function as well. We often “read” f′(x)f′(x) as “f prime of x”. Let’s compute a couple of derivatives using the definition. Let’s work one more example. This one will be a little different, but it’s got a point that needs to be made. In this...

Note that we replaced all the a’s in (1)(1) with x’s to acknowledge the fact that the derivative is really a function as well. We often “read” f′(x)f′(x) as “f prime of x”. Let’s compute a couple of derivatives using the definition. Let’s work one more example. This one will be a little different, but it’s got a point that needs to be made. In this...

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merriam-webster.com

https://www.merriam-webster.com/dictionary/derivative

derivative. noun. Medical Definition of derivative (Entry 2 of 2) 1 : something that is obtained from, grows out of, or results from an earlier or more fundamental state or condition. 2 …

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libretexts.org

https://math.libretexts.org/Bookshelves/Calculus/CLP-1_Differential_Calculus_(Feldman_Rechnitzer_and_Yeager)/03%3A_Derivatives/3.02%3A_Definition_of_the_Derivative

Nov 20, 2021 · The derivative as a function, f ′ (x) as defined in Definition 2.2.6. Of course, if we have f ′ (x) then we can always recover the derivative at a specific point by substituting x = a. As we noted at the beginning of the chapter, the derivative was discovered independently by Newton and Leibniz in the late 17th century.

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wikipedia.org

https://en.wikipedia.org/wiki/Derivative

Relative to a hyperreal extension R ⊂ R of the real numbers, the derivative of a real function y = f(x) at a real point x can be defined as the shadow of the quotient ∆y/∆x for infinitesimal ∆x, where ∆y = f(x + ∆x) − f(x). Here the natural extension of f to the hyperreals is still denoted f. Here the derivative is said to exist if the shadow is independent of the infinitesimal chosen.

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iit.edu

https://web.iit.edu/sites/web/files/departments/academic-affairs/academic-resource-center/pdfs/what_are_Derivative.pdf

Definition of Derivative •As we saw, as the change in x is made smaller and smaller, the value of the quotient – often called the Difference Quotient – comes closer and closer to 4. •The formal way of writing it is • ′2=lim 𝑓2+ℎ−𝑓(2) ℎ =4 •Think of the variable h as a “slider”. You

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math.net

https://www.math.net/derivative

Geometrically, the derivative is the slope of the line tangent to the curve at a point of interest. It is sometimes referred to as the instantaneous rate of change. Typically, we calculate the slope of a line using two points on the line. This is not possible for a curve, since the slope of a curve changes from point to point.

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