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Theorems · Theorem · real analysis

iteratedDeriv_one

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type u_2} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F}, iteratedDeriv 1 f = deriv f
Defined in
Mathlib.Analysis.Calculus.IteratedDeriv.Defs
Cited by
16 results in Mathlib
Foundations
Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpace

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Real.iteratedDeriv_add_one_cos · cited by 3Real.iteratedDeriv_add_on…Real.iteratedDeriv_add_one_cosh · cited by 3Real.iteratedDeriv_add_on…Real.iteratedDeriv_add_one_sin · cited by 3Real.iteratedDeriv_add_on…Real.iteratedDeriv_add_one_sinh · cited by 3Real.iteratedDeriv_add_on…Complex.iteratedDeriv_add_one_cos · cited by 3Complex.iteratedDeriv_add…Complex.iteratedDeriv_add_one_cosh · cited by 3Complex.iteratedDeriv_add…Complex.iteratedDeriv_add_one_sin · cited by 3Complex.iteratedDeriv_add…Complex.iteratedDeriv_add_one_sinh · cited by 3Complex.iteratedDeriv_add…AnalyticAt.analyticAt_localInverse · cited by 2AnalyticAt.analyticAt_loc…ModularForm.discriminant_qExpansion_coeff_one · cited by 2ModularForm.discriminant_…ProbabilityTheory.iteratedDeriv_two_cgf · cited by 1ProbabilityTheory.iterate…ProbabilityTheory.variance_fun_id_gaussianReal · cited by 1ProbabilityTheory.varianc…DiffContOnCl.deriv_eq_smul_circleIntegral · cited by 0DiffContOnCl.deriv_eq_smu…PeriodPair.deriv_derivWeierstrassPExcept_self · cited by 0PeriodPair.deriv_derivWei…DifferentiableOn.deriv_eq_smul_circleIntegral · cited by 0DifferentiableOn.deriv_eq…NormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldone_smul · cited by 1374one_smulderiv · cited by 676deriviteratedDeriv · cited by 188iteratedDerivfderiv_eq_smul_deriv · cited by 6fderiv_eq_smul_deriviteratedFDeriv_one_apply · cited by 2iteratedFDeriv_one_applyiteratedDeriv_oneCITED BYCITES

Cites8

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Cited by16

Results whose statement or proof uses this declaration.