Theorems · Theorem · field theory
Polynomial.derivative_monomial
∀ {R : Type u} [inst : Semiring R] (a : R) (n : ℕ),
Polynomial.derivative ((Polynomial.monomial n) a) = (Polynomial.monomial (n - 1)) (a * ↑n)- Defined in
- Mathlib.Algebra.Polynomial.Derivative
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 107 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.
Cites14
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
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Xproof · cited by 1,639
- MulZeroClass.zero_mulproof · cited by 1,625
- map_zeroproof · cited by 1,614
- Polynomial.Cproof · cited by 1,598
- Polynomial.derivativestatement · cited by 331
- Polynomial.monomialstatement and proof · cited by 256
- Polynomial.C_mul_X_pow_eq_monomialproof · cited by 53
Cited by8
Results whose statement or proof uses this declaration.
- Polynomial.derivative_mulproof · cited by 35
- Polynomial.derivative_Xproof · cited by 34
- Polynomial.hasStrictDerivAtproof · cited by 3
- Polynomial.derivative_compproof · cited by 2
- Polynomial.derivative_C_mul_X_powproof · cited by 2
- Derivation.apply_aeval_eq'proof · cited by 2
- Polynomial.derivative_bernoulli_add_oneproof · cited by 1
- Polynomial.derivative_monomial_succproof · cited by 1