Theorems · Theorem · real analysis
iteratedDeriv_succ
∀ {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}, iteratedDeriv (n + 1) f = deriv (iteratedDeriv n f)The n+1-th iterated derivative can be obtained by differentiating the n-th
iterated derivative.
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- derivstatement and proof · cited by 676
- iteratedDerivstatement and proof · cited by 188
- iteratedDerivWithinproof · cited by 122
- iteratedDerivWithin_univproof · cited by 16
- iteratedDerivWithin_succproof · cited by 11
- derivWithin_univproof · cited by 11
Cited by18
Results whose statement or proof uses this declaration.
- Real.iteratedDeriv_add_one_cosproof · cited by 3
- Real.iteratedDeriv_add_one_coshproof · cited by 3
- Real.iteratedDeriv_add_one_sinproof · cited by 3
- Real.iteratedDeriv_add_one_sinhproof · cited by 3
- Complex.iteratedDeriv_add_one_cosproof · cited by 3
- Complex.iteratedDeriv_add_one_coshproof · cited by 3
- Complex.iteratedDeriv_add_one_sinproof · cited by 3
- Complex.iteratedDeriv_add_one_sinhproof · cited by 3
- iteratedDeriv_comp_add_constproof · cited by 2
- ProbabilityTheory.iteratedDeriv_mgfproof · cited by 2
- ProbabilityTheory.iteratedDeriv_two_cgfproof · cited by 1
- LSeries_iteratedDerivproof · cited by 1