Theorems · Theorem · real analysis

deriv_comp_of_eq

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] (x : 𝕜) {𝕜' : Type u_1} [inst_1 : NontriviallyNormedField 𝕜']
  [inst_2 : NormedAlgebra 𝕜 𝕜'] {h : 𝕜 → 𝕜'} {h₂ : 𝕜' → 𝕜'} {y : 𝕜'},
  DifferentiableAt 𝕜' h₂ y → DifferentiableAt 𝕜 h x → h x = y → deriv (h₂ ∘ h) x = deriv h₂ (h x) * deriv h 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