Theorems · Theorem · field theory
Polynomial.derivative_prod_finset
∀ {R : Type u} {ι : Type y} [inst : CommSemiring R] [inst_1 : DecidableEq ι] {s : Finset ι} {f : ι → Polynomial R},
Polynomial.derivative (∏ b ∈ s, f b) = ∑ a ∈ s, (∏ b ∈ s.erase a, f b) * Polynomial.derivative (f a)- Defined in
- Mathlib.Algebra.Polynomial.Derivative
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Finsetstatement and proof · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Polynomialstatement and proof · cited by 5,681
- Finset.sumstatement · cited by 5,195
- Finset.prodstatement · cited by 2,356
- Finset.erasestatement · cited by 455
- Polynomial.derivativestatement · cited by 331
- Polynomial.derivative_prodproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.iterate_derivative_prod_X_sub_Cproof · cited by 0