Derivative function

Builds on Derivative Differentiable function

Definition

Let $I$ be an open interval and let $f \colon I \to \mathbb{R}$ be differentiable on $I$ . The derivative function of $f$ is the function $f' \colon I \to \mathbb{R}$ that maps each $x \in I$ to the derivative $f'(x)$ of $f$ at $x$ .

Remarks

Other notations are $\frac{df}{dx}$ and $D f$ . For example, the derivative function of $x^3$ is $3 x^2$ . The derivative function need not be continuous. See x^2 sin(1/x). Mathlib defines deriv f on all of $\mathbb{R}$ , with value $0$ at points where $f$ is not differentiable.

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Limit point of a set definition
Limit of a function definition
Derivative definition
Differentiable function definition
Derivative function definition

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64 pages build on this one.

Tag	`027K9RMZ43`
URI	`m2://027K9RMZ43`
Kind	definition
Writing	W0 stub
MSC	26A24
Defines	Derivative function
Uses	Derivative, Differentiable function

Derivative function

Definition

Remarks

Reading path

Where this leads

Further reading

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