Theorems · Theorem · commutative algebra
MvPolynomial.pderiv_pow
∀ {R : Type u} {σ : Type v} [inst : CommSemiring R] {i : σ} {f : MvPolynomial σ R} {n : ℕ},
(MvPolynomial.pderiv i) (f ^ n) = ↑n * f ^ (n - 1) * (MvPolynomial.pderiv i) f- Defined in
- Mathlib.Algebra.MvPolynomial.PDeriv
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- mul_assocproof · cited by 1,667
- nsmul_eq_mulproof · cited by 369
- smul_eq_mulproof · cited by 357
- Derivationstatement · cited by 293
- MvPolynomial.pderivstatement and proof · cited by 71
- Derivation.leibniz_powproof · cited by 10
Cited by6
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Projective.polynomialZ_eqproof · cited by 1
- WeierstrassCurve.Jacobian.polynomialZ_eqproof · cited by 1
- WeierstrassCurve.Projective.polynomialY_eqproof · cited by 1
- WeierstrassCurve.Jacobian.polynomialX_eqproof · cited by 1
- WeierstrassCurve.Projective.polynomialX_eqproof · cited by 1
- WeierstrassCurve.Jacobian.polynomialY_eqproof · cited by 1