Theorems · Theorem · global analysis

HasStrictFDerivAt.comp

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {G : Type u_4}
  [inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace 𝕜 G] {f : E → F} {f' : E →L[𝕜] F} (x : E) {g : F → G}
  {g' : F →L[𝕜] G},
  HasStrictFDerivAt g g' (f x) → HasStrictFDerivAt f f' x → HasStrictFDerivAt (fun x => g (f x)) (g' ∘SL f') x

The chain rule for derivatives in the sense of strict differentiability.

Defined in

Mathlib.Analysis.Calculus.FDeriv.Comp

Cited by

37 results in Mathlib

Foundations

Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace