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Theorems · Theorem · real analysis

derivWithin_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 (c * d) s x = derivWithin c s x * d x + c x * derivWithin d s x
Defined in
Mathlib.Analysis.Calculus.Deriv.Mul
Cited by
0 results in Mathlib
Foundations
Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedRingNormedAlgebra
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Set · cited by 53352SetNontriviallyNormedField · cited by 8742NontriviallyNormedFieldNormedAlgebra · cited by 1165NormedAlgebraNormedRing · cited by 924NormedRingDifferentiableWithinAt · cited by 453DifferentiableWithinAtderivWithin · cited by 258derivWithinderivWithin_fun_mul · cited by 2derivWithin_fun_mulderivWithin_mulCITED BYCITES

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