Evaluation of the derivative of a polynomial sum

Proved

WorkbookRestored.plus_28668

by wamlart · Sep 12, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

lean-workbookrestored-importssource-checked

For real polynomials $p,q$ and a real $x$ , $(p+q)\prime(x)=p\prime(x)+q\prime(x)$ .

This restores the missing imports or namespaces of the original node, retaining its formal proposition. Source: Lean-Workbook row lean_workbook_plus_28668 (Apache-2.0).

Preamble

import Mathlib.Analysis.Complex.Basic
import Mathlib.Algebra.Polynomial.Derivative
import Mathlib.Algebra.Polynomial.Eval.Defs
import Mathlib.Algebra.Polynomial.Roots
open Polynomial

Formal statement

theorem WorkbookRestored.plus_28668 (p q : Polynomial ℝ) (x : ℝ) :
  (p + q).derivative.eval x = p.derivative.eval x + q.derivative.eval x   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_28668; original Prove2Me node 5ad46e0d-a0ec-45b4-a8ce-53b6c0d7ed35; Apache-2.0

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