Theorems · Definition · functional analysis

fderiv

(𝕜 : Type u_4) →
  [inst : NontriviallyNormedField 𝕜] →
    {E : Type u_5} →
      [inst_1 : AddCommGroup E] →
        [inst_2 : Module 𝕜 E] →
          [inst_3 : TopologicalSpace E] →
            {F : Type u_6} →
              [inst_4 : AddCommGroup F] →
                [inst_5 : Module 𝕜 F] → [inst_6 : TopologicalSpace F] → (E → F) → E → E →L[𝕜] F

If f has a derivative at x, then fderiv 𝕜 f x is such a derivative. Otherwise, it is set to 0.

Defined in

Mathlib.Analysis.Calculus.FDeriv.Defs

Cited by

398 results in Mathlib

Foundations

Depth 79 from the axioms, rests on 1,036 definitions · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldAddCommGroupModuleTopologicalSpaceAddCommGroupModuleTopologicalSpace