Theorems · Theorem · real analysis
DifferentiableWithinAt.rpow
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f g : E → ℝ} {x : E} {s : Set E},
DifferentiableWithinAt ℝ f s x →
DifferentiableWithinAt ℝ g s x → f x ≠ 0 → DifferentiableWithinAt ℝ (fun x => f x ^ g x) s x- Cited by
- 1 results in Mathlib
- Foundations
- Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- DifferentiableWithinAtstatement and proof · cited by 453
- DifferentiableAt.comp_differentiableWithinAtproof · cited by 14
- DifferentiableWithinAt.prodMkproof · cited by 6
- Real.differentiableAt_rpow_of_neproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- DifferentiableOn.rpowproof · cited by 0