Theorems · Theorem · real analysis
iteratedDeriv_comp_neg
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type u_2} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] (n : ℕ) (f : 𝕜 → F) (a : 𝕜),
iteratedDeriv n (fun x => f (-x)) a = (-1) ^ n • iteratedDeriv n f (-a)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Set.univproof · cited by 3,945
- smul_applyproof · cited by 229
- iteratedDerivstatement · cited by 188
- iteratedFDerivWithinproof · cited by 147
- iteratedFDerivWithin_comp_negproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Differentiable.apply_le_of_iteratedDeriv_alternatingproof · cited by 1
- iteratedDeriv_comp_const_subproof · cited by 0