Theorems · Theorem · real analysis

HasDerivAt.comp_hasFDerivAt

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {E : Type w} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {𝕜' : Type u_1} [inst_3 : NontriviallyNormedField 𝕜'] [inst_4 : NormedAlgebra 𝕜 𝕜']
  {h₂ : 𝕜' → 𝕜'} {h₂' : 𝕜'} {f : E → 𝕜'} {f' : E →L[𝕜] 𝕜'} (x : E),
  HasDerivAt h₂ h₂' (f x) → HasFDerivAt f f' x → HasFDerivAt (h₂ ∘ f) (h₂' • f') x

Defined in

Mathlib.Analysis.Calculus.Deriv.Comp

Cited by

20 results in Mathlib

Foundations

Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNontriviallyNormedFieldNormedAlgebra