Theorems · Theorem · real analysis
DifferentiableAt.const_mul
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {x : E} {𝔸 : Type u_5} [inst_3 : NormedRing 𝔸] [inst_4 : NormedAlgebra 𝕜 𝔸] {a : E → 𝔸},
DifferentiableAt 𝕜 a x → ∀ (b : 𝔸), DifferentiableAt 𝕜 (fun y => b * a y) x- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Mul
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 178 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
- NormedAlgebrastatement and proof · cited by 1,165
- NormedRingstatement and proof · cited by 924
- DifferentiableAtstatement and proof · cited by 617
- DifferentiableAt.hasFDerivAtproof · cited by 134
- HasFDerivAt.differentiableAtproof · cited by 83
- HasFDerivAt.const_mulproof · cited by 4
Cited by12
Results whose statement or proof uses this declaration.
- Differentiable.const_mulproof · cited by 8
- ProbabilityTheory.integral_id_gaussianRealproof · cited by 6
- not_differentiableAt_norm_zeroproof · cited by 4
- ZMod.differentiableAt_LFunctionproof · cited by 3
- Complex.Gamma_mul_Gamma_add_halfproof · cited by 2
- ModularForm.logDeriv_qParamproof · cited by 1
- Real.hasDerivAt_Gamma_one_halfproof · cited by 1
- logDeriv_sin_div_eq_cotproof · cited by 1
- ProbabilityTheory.variance_fun_id_gaussianRealproof · cited by 1
- Real.differentiableAt_mulExpNegMulSqproof · cited by 1
- jacobiTheta₂'_functional_equationproof · cited by 1
- ModularForm.logDeriv_one_sub_mul_cexp_compproof · cited by 0