Theorems · Theorem · functional analysis
hasStrictDerivAt_exp_smul_const_of_mem_ball
∀ {𝕂 : Type u_1} {𝔸 : Type u_3} [inst : NontriviallyNormedField 𝕂] [CharZero 𝕂] [inst_2 : NormedRing 𝔸]
[inst_3 : NormedAlgebra 𝕂 𝔸] [CompleteSpace 𝔸] (x : 𝔸) (t : 𝕂),
t • x ∈ Metric.eball 0 (NormedSpace.expSeries 𝕂 𝔸).radius →
HasStrictDerivAt (fun u => NormedSpace.exp (u • x)) (NormedSpace.exp (t • x) * x) t- Cited by
- 2 results in Mathlib
- Foundations
- Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- CompleteSpacestatement and proof · cited by 2,532
- one_smulproof · cited by 1,374
- NormedAlgebrastatement and proof · cited by 1,165
- CharZerostatement and proof · cited by 932
- NormedRingstatement and proof · cited by 924
- Metric.eballstatement and proof · cited by 294
- smul_applyproof · cited by 229
- HasStrictDerivAtstatement · cited by 163
- NormedSpace.expstatement and proof · cited by 157
Cited by2
Results whose statement or proof uses this declaration.
- hasDerivAt_exp_smul_const_of_mem_ballproof · cited by 1
- hasStrictDerivAt_exp_smul_constproof · cited by 0