Theorems · Theorem · global analysis

HasFPowerSeriesAt.deriv

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {p : FormalMultilinearSeries 𝕜 𝕜 F} {f : 𝕜 → F} {x : 𝕜},
  HasFPowerSeriesAt f p x → deriv f x = (p 1) fun x => 1

Defined in: Mathlib.Analysis.Calculus.FDeriv.Analytic
Cited by: 1 results in Mathlib
Foundations: Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NontriviallyNormedField NormedAddCommGroup NormedSpace

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Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement · 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
ContinuousMultilinearMapstatement · cited by 1,016
derivstatement · cited by 676
FormalMultilinearSeriesstatement and proof · cited by 615
HasDerivAt.derivproof · cited by 147
HasFPowerSeriesAtstatement and proof · cited by 94
HasFPowerSeriesAt.hasDerivAtproof · cited by 1

Cited by1

Results whose statement or proof uses this declaration.

HasFPowerSeriesAt.has_fpower_series_dslope_fslopeproof · cited by 1