Theorems · Theorem · real analysis

HasDerivAt.continuousAt_div

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] [inst_1 : DecidableEq 𝕜] {f : 𝕜 → 𝕜} {c a : 𝕜},
  HasDerivAt f a c → ContinuousAt (Function.update (fun x => (f x - f c) / (x - c)) c a) c

Defined in

Mathlib.Analysis.Calculus.Deriv.Slope

Cited by

0 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldDecidableEq