Theorems · Theorem · real analysis

HasDerivAt.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},
  HasDerivAt c c' x → HasDerivAt d d' x → HasDerivAt (fun i => c i * d i) (c' * d x + c x * d') x

Eta-expanded form of HasDerivAt.mul

Defined in: Mathlib.Analysis.Calculus.Deriv.Mul
Cited by: 1 results in Mathlib
Foundations: Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NontriviallyNormedField NormedRing NormedAlgebra

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

NontriviallyNormedFieldstatement · cited by 8,742
NormedAlgebrastatement · cited by 1,165
NormedRingstatement · cited by 924
HasDerivAtstatement · cited by 493
HasDerivAt.mulproof · cited by 20

Cited by1

Results whose statement or proof uses this declaration.

EulerSine.integral_sin_mul_sin_mul_cos_pow_eqproof · cited by 1