Theorems · Theorem · field theory
Polynomial.derivative_add
∀ {R : Type u} [inst : Semiring R] {f g : Polynomial R},
Polynomial.derivative (f + g) = Polynomial.derivative f + Polynomial.derivative g- Defined in
- Mathlib.Algebra.Polynomial.Derivative
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 106 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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.derivativestatement and proof · cited by 331
- LinearMap.map_addproof · cited by 32
Cited by9
Results whose statement or proof uses this declaration.
- Polynomial.hasStrictDerivAtproof · cited by 3
- Polynomial.derivative_compproof · cited by 2
- Derivation.map_aevalproof · cited by 2
- Polynomial.derivative_X_add_Cproof · cited by 2
- Polynomial.Bivariate.pderiv_one_equivMvPolynomialproof · cited by 1
- Polynomial.separable_X_add_Cproof · cited by 1
- Polynomial.derivative_eval₂_Cproof · cited by 1
- WeierstrassCurve.Affine.nonsingular_negAdd_of_eval_derivative_ne_zeroproof · cited by 1