Theorems · Theorem · global analysis

fderiv_const_smul_of_invertible

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F}
  {x : E} {R : Type u_4} [inst_5 : Monoid R] [inst_6 : DistribMulAction R F] [inst_7 : SMulCommClass 𝕜 R F]
  [inst_8 : ContinuousConstSMul R F] (c : R) [Invertible c], fderiv 𝕜 (c • f) x = c • fderiv 𝕜 f x

A version of fderiv_const_smul without differentiability hypothesis: in return, the constant c must be invertible, i.e. if R is a field.

Defined in

Mathlib.Analysis.Calculus.FDeriv.Add

Cited by

0 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceMonoidDistribMulActionSMulCommClassContinuousConstSMulInvertible