Theorems · Theorem · real analysis

HasFDerivAt.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_6} [inst_3 : NormedCommRing 𝔸'] [inst_4 : NormedAlgebra 𝕜 𝔸']
  {c d : E → 𝔸'} {c' d' : E →L[𝕜] 𝔸'},
  HasFDerivAt c c' x → HasFDerivAt d d' x → HasFDerivAt (c * d) (c x • d' + d x • c') x

Defined in

Mathlib.Analysis.Calculus.FDeriv.Mul

Cited by

4 results in Mathlib

Foundations

Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedCommRingNormedAlgebra