Theorems · Theorem · field theory
Polynomial.derivative_comp
∀ {R : Type u} [inst : CommSemiring R] (p q : Polynomial R),
Polynomial.derivative (p.comp q) = Polynomial.derivative q * (Polynomial.derivative p).comp q- Defined in
- Mathlib.Algebra.Polynomial.Derivative
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 111 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.
Cites21
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
- Polynomialstatement and proof · cited by 5,681
- zero_addproof · cited by 2,366
- MulZeroClass.zero_mulproof · cited by 1,625
- Polynomial.Cproof · cited by 1,598
- map_mulproof · cited by 1,137
- mul_addproof · cited by 413
- Polynomial.derivativestatement and proof · cited by 331
- Polynomial.compstatement and proof · cited by 193
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.iterate_derivative_comp_one_sub_Xproof · cited by 3
- Polynomial.derivative_comp_one_sub_Xproof · cited by 0