Theorems · Theorem · real analysis

HasDerivWithinAt.mul

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {x : 𝕜} {s : Set 𝕜} {𝔸 : Type u_3} [inst_1 : NormedRing 𝔸]
  [inst_2 : NormedAlgebra 𝕜 𝔸] {c d : 𝕜 → 𝔸} {c' d' : 𝔸},
  HasDerivWithinAt c c' s x → HasDerivWithinAt d d' s x → HasDerivWithinAt (c * d) (c' * d x + c x * d') s x

Defined in

Mathlib.Analysis.Calculus.Deriv.Mul

Cited by

7 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedRingNormedAlgebra