# Real derivatives at a point and finite difference quotients

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.

[Catalogue presentation and source-binding data](https://ocme.evemisslab.com/data/i18n/catalogue.en.json)



## [Real derivatives at a point and finite difference quotients](https://ocme.evemisslab.com/en/atlas/atlas-derivative/)

A derivative is the two-sided limit of nonzero-step quotients, not any one finite-step quotient; an absolute-value corner retains nonexistence.

atlas-derivative · canonical_mko

[Real derivatives at a point and finite difference quotients](https://ocme.evemisslab.com/en/mko/mko-derivative/)

## Prerequisite nodes


- [Function limits on punctured real domains](https://ocme.evemisslab.com/en/atlas/atlas-function-limit/)
- [Average rate of change between distinct inputs](https://ocme.evemisslab.com/en/atlas/atlas-rate-of-change/)
- [Univariate polynomials over the rationals](https://ocme.evemisslab.com/en/atlas/atlas-polynomial/)
- [Absolute value](https://ocme.evemisslab.com/en/atlas/atlas-absolute-value/)