Theorems · Theorem · global analysis

HasDerivAt.inner

∀ (𝕜 : Type u_1) {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  [inst_3 : NormedSpace ℝ E] {f g : ℝ → E} {f' g' : E} {x : ℝ},
  HasDerivAt f f' x →
    HasDerivAt g g' x → HasDerivAt (fun t => inner 𝕜 (f t) (g t)) (inner 𝕜 (f x) g' + inner 𝕜 f' (g x)) x

Defined in: Mathlib.Analysis.InnerProductSpace.Calculus
Cited by: 1 results in Mathlib
Foundations: Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: RCLike NormedAddCommGroup InnerProductSpace NormedSpace

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Cites8

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

Realstatement and proof · cited by 25,697
NormedAddCommGroupstatement and proof · cited by 15,752
NormedSpacestatement and proof · cited by 12,499
InnerProductSpacestatement and proof · cited by 3,523
RCLikestatement and proof · cited by 2,829
Inner.innerstatement · cited by 1,089
HasDerivAtstatement · cited by 493
HasDerivWithinAt.innerproof · cited by 1

Cited by1

Results whose statement or proof uses this declaration.

deriv_inner_applyproof · cited by 0