Theorems · Theorem · real analysis

derivWithin_comp_of_eq

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] (x : 𝕜) {s : Set 𝕜} {𝕜' : Type u_1}
  [inst_1 : NontriviallyNormedField 𝕜'] [inst_2 : NormedAlgebra 𝕜 𝕜'] {s' : Set 𝕜'} {h : 𝕜 → 𝕜'} {h₂ : 𝕜' → 𝕜'}
  {y : 𝕜'},
  DifferentiableWithinAt 𝕜' h₂ s' y →
    DifferentiableWithinAt 𝕜 h s x →
      Set.MapsTo h s s' → h x = y → derivWithin (h₂ ∘ h) s x = derivWithin h₂ s' (h x) * derivWithin h s x

Defined in

Mathlib.Analysis.Calculus.Deriv.Comp

Cited by

0 results in Mathlib

Foundations

Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNontriviallyNormedFieldNormedAlgebra