Theorems · Theorem · commutative algebra

Differential.deriv_aeval_eq

∀ {A : Type u_1} [inst : CommRing A] [inst_1 : Differential A] {R : Type u_2} [inst_2 : CommRing R]
  [inst_3 : Differential R] [inst_4 : Algebra A R] [DifferentialAlgebra A R] (x : R) (p : Polynomial A),
  ((Polynomial.aeval x) p)′ =
    (Polynomial.aeval x) (Differential.mapCoeffs p) + (Polynomial.aeval x) (Polynomial.derivative p) * x′

Defined in

Mathlib.RingTheory.Derivation.MapCoeffs

Cited by

2 results in Mathlib

Foundations

Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingDifferentialCommRingDifferentialAlgebraDifferentialAlgebra