Theorems · Theorem · global analysis
Differentiable.differentiableAt
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
[inst_3 : TopologicalSpace E] {F : Type u_3} [inst_4 : AddCommGroup F] [inst_5 : Module 𝕜 F]
[inst_6 : TopologicalSpace F] {f : E → F} {x : E}, Differentiable 𝕜 f → DifferentiableAt 𝕜 f x- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Basic
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- DifferentiableAtstatement · cited by 617
- Differentiablestatement and proof · cited by 298
Cited by32
Results whose statement or proof uses this declaration.
- ContinuousLinearEquiv.comp_differentiableWithinAt_iffproof · cited by 7
- Differentiable.comp_mdifferentiableWithinAtproof · cited by 6
- SchwartzMap.differentiableAtproof · cited by 3
- HurwitzZeta.differentiableAt_hurwitzZetaEven_sub_one_divproof · cited by 3
- MDifferentiableWithinAt.clm_applyproof · cited by 3
- ModularForm.differentiableAt_eta_tprodproof · cited by 2
- HurwitzZeta.differentiableAt_cosZetaproof · cited by 2
- TestFunction.lineDerivCLM_applyproof · cited by 2
- HurwitzZeta.differentiableAt_update_of_residueproof · cited by 2
- VectorFourier.fourierIntegral_fderivproof · cited by 2
- HasCompactSupport.hasFDerivAt_convolution_rightproof · cited by 2
- DifferentiableAt.deriv_comp_add_smulproof · cited by 2