Theorems · Theorem · functional analysis
fderiv_def
∀ (𝕜 : Type u_4) [inst : NontriviallyNormedField 𝕜] {E : Type u_5} [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
[inst_3 : TopologicalSpace E] {F : Type u_6} [inst_4 : AddCommGroup F] [inst_5 : Module 𝕜 F]
[inst_6 : TopologicalSpace F] (f : E → F) (x : E), fderiv 𝕜 f x = fderivWithin 𝕜 f Set.univ x- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- RingHom.idstatement · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousLinearMapstatement · cited by 5,352
- Set.univstatement and proof · cited by 3,945
- fderivstatement · cited by 398
- fderivWithinstatement and proof · cited by 357
Cited by5
Results whose statement or proof uses this declaration.
- DifferentiableAt.hasFDerivAtproof · cited by 134
- fderivWithin_univproof · cited by 29
- fderiv_zero_of_not_differentiableAtproof · cited by 9
- VectorField.lieBracket_smul_rightproof · cited by 1
- fderiv_const_applyproof · cited by 0