---
tag: 0EGN1E1JPB
kind: concept
name: Formal derivative
msc: [13N15]
sources:
  - url: https://en.wikipedia.org/wiki/Formal_derivative
    locator: lead section
same_as:
  wikidata: Q1955819
  wikipedia: Formal derivative
---

## Summary

The formal derivative of a polynomial is defined by the usual rule of calculus, $(x^n)' = n x^{n-1}$, with no limits.
It makes sense over every ring.
The [[definition of the formal derivative|0AD4VS02H3]] gives the formula.