Theorems · Theorem · field theory
Polynomial.derivative_C_mul_X_pow
∀ {R : Type u} [inst : Semiring R] (a : R) (n : ℕ),
Polynomial.derivative (Polynomial.C a * Polynomial.X ^ n) = Polynomial.C (a * ↑n) * Polynomial.X ^ (n - 1)- Defined in
- Mathlib.Algebra.Polynomial.Derivative
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 108 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.
Cites12
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
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- Polynomial.derivativestatement and proof · cited by 331
- Polynomial.monomialproof · cited by 256
- Polynomial.C_mul_X_pow_eq_monomialproof · cited by 53
- Polynomial.derivative_monomialproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.derivative_X_powproof · cited by 13
- Polynomial.derivative_C_mul_X_sqproof · cited by 0