Theorems · Theorem · functional analysis
hasStrictFDerivAt_exp_smul_const
∀ (𝕂 : Type u_1) {𝕊 : Type u_2} {𝔸 : Type u_3} [inst : RCLike 𝕂] [inst_1 : NormedCommRing 𝕊] [inst_2 : NormedRing 𝔸]
[inst_3 : NormedAlgebra 𝕂 𝕊] [inst_4 : NormedAlgebra 𝕂 𝔸] [inst_5 : Algebra 𝕊 𝔸] [inst_6 : ContinuousSMul 𝕊 𝔸]
[inst_7 : IsScalarTower 𝕂 𝕊 𝔸] [CompleteSpace 𝔸] (x : 𝔸) (t : 𝕊),
HasStrictFDerivAt (fun u => NormedSpace.exp (u • x)) (NormedSpace.exp (t • x) • ContinuousLinearMap.smulRight 1 x) t- Cited by
- 0 results in Mathlib
- Foundations
- Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- Algebrastatement and proof · cited by 11,388
- ContinuousLinearMapstatement · cited by 5,352
- IsScalarTowerstatement and proof · cited by 3,896
- RCLikestatement and proof · cited by 2,829
- CompleteSpacestatement and proof · cited by 2,532
- NormedAlgebrastatement and proof · cited by 1,165
- ContinuousSMulstatement and proof · cited by 1,016
- NormedRingstatement and proof · cited by 924
- HasStrictFDerivAtstatement · cited by 261
- NormedCommRingstatement and proof · cited by 218
- NormedSpace.expstatement · cited by 157
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