Theorems · Theorem · field theory
Polynomial.derivative_X_pow
∀ {R : Type u} [inst : Semiring R] (n : ℕ),
Polynomial.derivative (Polynomial.X ^ n) = Polynomial.C ↑n * Polynomial.X ^ (n - 1)- Defined in
- Mathlib.Algebra.Polynomial.Derivative
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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 and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement and proof · cited by 10,215
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- one_mulproof · cited by 2,841
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- map_oneproof · cited by 861
- DFunLikeproof · cited by 576
- Polynomial.derivativestatement and proof · cited by 331
Cited by13
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.discr_prime_pow_ne_twoproof · cited by 4
- FiniteField.roots_X_pow_card_sub_Xproof · cited by 2
- Polynomial.separable_C_mul_X_pow_add_C_mul_X_add_Cproof · cited by 2
- isCoveringMapOn_npowproof · cited by 1
- Polynomial.Chebyshev.add_one_mul_T_eq_poly_in_Uproof · cited by 1
- galois_poly_separableproof · cited by 1
- Polynomial.iterate_derivative_X_pow_eq_natCast_mulproof · cited by 1
- WeierstrassCurve.Affine.nonsingular_negAdd_of_eval_derivative_ne_zeroproof · cited by 1
- Polynomial.X_pow_sub_C_separable_iffproof · cited by 1
- Polynomial.derivative_X_pow_succproof · cited by 1