Theorems · Theorem · field theory
Polynomial.derivative_pow_succ
∀ {R : Type u} [inst : CommSemiring R] (p : Polynomial R) (n : ℕ),
Polynomial.derivative (p ^ (n + 1)) = Polynomial.C (↑n + 1) * p ^ n * Polynomial.derivative p- Defined in
- Mathlib.Algebra.Polynomial.Derivative
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 109 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.
Cites26
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
- RingHom.idstatement · cited by 18,349
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
- zero_addproof · cited by 2,366
- Nat.cast_zeroproof · cited by 1,870
- mul_assocproof · cited by 1,667
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.derivative_powproof · cited by 11
- Polynomial.derivative_sqproof · cited by 3
- divRadical_dvd_derivativeproof · cited by 1