Theorems · Theorem · real analysis

deriv_comp

∀ {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'},
  DifferentiableAt 𝕜' h₂ (h x) → DifferentiableAt 𝕜 h x → deriv (h₂ ∘ h) x = deriv h₂ (h x) * deriv h x

Defined in

Mathlib.Analysis.Calculus.Deriv.Comp

Cited by

8 results in Mathlib

Foundations

Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNontriviallyNormedFieldNormedAlgebra