Theorems · Theorem · functional analysis
hasDerivAt_exp_zero_of_radius_pos
∀ {𝕂 : Type u_1} [inst : NontriviallyNormedField 𝕂] [CompleteSpace 𝕂] [CharZero 𝕂],
0 < (NormedSpace.expSeries 𝕂 𝕂).radius → HasDerivAt NormedSpace.exp 1 0The exponential map in a complete normed field 𝕂 of characteristic zero has derivative
1 at zero, as long as it converges on a neighborhood of zero.
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- Foundations
- Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement · cited by 9,879
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- CompleteSpacestatement and proof · cited by 2,532
- CharZerostatement and proof · cited by 932
- HasDerivAtstatement · cited by 493
- NormedSpace.expstatement · cited by 157
- FormalMultilinearSeries.radiusstatement and proof · cited by 150
- NormedSpace.expSeriesstatement and proof · cited by 68
- HasStrictDerivAt.hasDerivAtproof · cited by 52
- hasStrictDerivAt_exp_zero_of_radius_posproof · cited by 2
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