Theorems · Theorem · real analysis
HasStrictDerivAt.hasDerivAt
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {f' : F} {x : 𝕜}, HasStrictDerivAt f f' x → HasDerivAt f f' x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Basic
- Cited by
- 52 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- HasDerivAtstatement · cited by 493
- HasStrictDerivAtstatement and proof · cited by 163
- HasStrictFDerivAt.hasFDerivAtproof · cited by 43
- HasStrictDerivAt.hasStrictFDerivAtproof · cited by 21
Cited by52
Results whose statement or proof uses this declaration.
- Real.hasDerivAt_sinproof · cited by 14
- Real.hasDerivAt_rpow_constproof · cited by 11
- Real.hasDerivAt_logproof · cited by 10
- Complex.hasDerivAt_cosproof · cited by 10
- Complex.hasDerivAt_sinproof · cited by 10
- hasDerivAt_invproof · cited by 9
- hasDerivAt_powproof · cited by 8
- Complex.hasDerivAt_sinhproof · cited by 8
- Real.hasDerivAt_arctanproof · cited by 7
- Polynomial.hasDerivAtproof · cited by 7
- Complex.hasDerivAt_coshproof · cited by 7
- Real.hasDerivAt_sqrtproof · cited by 6