Theorems · Theorem · real analysis
derivWithin_fun_mul
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {x : 𝕜} {s : Set 𝕜} {𝔸 : Type u_3} [inst_1 : NormedRing 𝔸]
[inst_2 : NormedAlgebra 𝕜 𝔸] {c d : 𝕜 → 𝔸},
DifferentiableWithinAt 𝕜 c s x →
DifferentiableWithinAt 𝕜 d s x →
derivWithin (fun y => c y * d y) s x = derivWithin c s x * d x + c x * derivWithin d s x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Mul
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- NormedAddCommGroupproof · cited by 15,752
- NormedSpaceproof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- add_zeroproof · cited by 2,707
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- NormedAlgebrastatement and proof · cited by 1,165
- NormedRingstatement and proof · cited by 924
- DifferentiableWithinAtstatement and proof · cited by 453
- derivWithinstatement · cited by 258
- UniqueDiffWithinAtproof · cited by 252
Cited by2
Results whose statement or proof uses this declaration.
- ModularForm.discriminant_qExpansion_coeff_oneproof · cited by 2
- derivWithin_mulproof · cited by 0