Theorems · Theorem · real analysis
dslope_sub_smul
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] [inst_3 : DecidableEq 𝕜] (f : 𝕜 → E) (a : 𝕜),
dslope (fun x => (x - a) • f x) a = Function.update f a (deriv (fun x => (x - a) • f x) a)- Defined in
- Mathlib.Analysis.Calculus.DSlope
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 109 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.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- derivstatement · cited by 676
- Function.updatestatement · cited by 502
- dslopestatement · cited by 40
- dslope_sameproof · cited by 6
- Function.eq_update_iffproof · cited by 3
- eqOn_dslope_sub_smulproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Complex.differentiableOn_update_limUnder_of_isLittleOproof · cited by 4