Theorems · Theorem · global analysis

mdifferentiableAt_iff_differentiableAt

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {E' : Type u_3} [inst_3 : NormedAddCommGroup E'] [inst_4 : NormedSpace 𝕜 E'] {f : E → E'}
  {x : E}, MDiffAt f x ↔ DifferentiableAt 𝕜 f x

For maps between vector spaces, MDifferentiableAt and DifferentiableAt coincide

Defined in

Mathlib.Geometry.Manifold.MFDeriv.FDeriv

Cited by

4 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace