Theorems · Theorem · real analysis
DifferentiableAt.div
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {x : 𝕜} {𝕜' : Type u_1} [inst_1 : NontriviallyNormedField 𝕜']
[inst_2 : NormedAlgebra 𝕜 𝕜'] {c d : 𝕜 → 𝕜'},
DifferentiableAt 𝕜 c x → DifferentiableAt 𝕜 d x → d x ≠ 0 → DifferentiableAt 𝕜 (c / d) x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Inv
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 189 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.
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- NormedAlgebrastatement and proof · cited by 1,165
- DifferentiableAtstatement and proof · cited by 617
- DifferentiableAt.hasDerivAtproof · cited by 114
- HasDerivAt.differentiableAtproof · cited by 73
- HasDerivAt.divproof · cited by 7
Cited by7
Results whose statement or proof uses this declaration.
- DifferentiableAt.fun_divproof · cited by 4
- tendsto_riemannZeta_sub_one_divproof · cited by 3
- ZMod.differentiableAt_completedLFunctionproof · cited by 3
- PeriodPair.eqOn_deriv_weierstrassPExcept_derivWeierstrassPExceptproof · cited by 3
- HurwitzZeta.differentiableAt_hurwitzZetaEven_sub_one_divproof · cited by 3
- Differentiable.divproof · cited by 1