Theorems · Theorem · real analysis

HasFDerivAt.const_mul

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {x : E} {𝔸 : Type u_5} [inst_3 : NormedRing 𝔸] [inst_4 : NormedAlgebra 𝕜 𝔸] {a : E → 𝔸}
  {a' : E →L[𝕜] 𝔸}, HasFDerivAt a a' x → ∀ (b : 𝔸), HasFDerivAt (fun y => b * a y) (b • a') x

Defined in

Mathlib.Analysis.Calculus.FDeriv.Mul

Cited by

4 results in Mathlib

Foundations

Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedRingNormedAlgebra