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Theorems · Theorem · real analysis

HasStrictDerivAt.fun_mul

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {x : 𝕜} {𝔸 : Type u_3} [inst_1 : NormedRing 𝔸]
  [inst_2 : NormedAlgebra 𝕜 𝔸] {c d : 𝕜 → 𝔸} {c' d' : 𝔸},
  HasStrictDerivAt c c' x → HasStrictDerivAt d d' x → HasStrictDerivAt (fun i => c i * d i) (c' * d x + c x * d') x

Eta-expanded form of HasStrictDerivAt.mul

Defined in
Mathlib.Analysis.Calculus.Deriv.Mul
Cited by
1 results in Mathlib
Foundations
Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedRingNormedAlgebra
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

HasStrictDerivAt.fun_div · cited by 1HasStrictDerivAt.fun_divNontriviallyNormedField · cited by 8742NontriviallyNormedFieldNormedAlgebra · cited by 1165NormedAlgebraNormedRing · cited by 924NormedRingHasStrictDerivAt · cited by 163HasStrictDerivAtHasStrictDerivAt.mul · cited by 3HasStrictDerivAt.mulHasStrictDerivAt.fun_mulCITED BYCITES

Cites5

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Cited by1

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