Theorems · Theorem · real analysis
ContDiffAt.rpow
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f g : E → ℝ} {x : E} {n : WithTop ℕ∞},
ContDiffAt ℝ n f x → ContDiffAt ℝ n g x → f x ≠ 0 → ContDiffAt ℝ n (fun x => f x ^ g x) x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- ENatstatement and proof · cited by 4,985
- WithTopstatement and proof · cited by 3,754
- ContDiffAtstatement and proof · cited by 262
- ContDiffAt.compproof · cited by 34
- ContDiffAt.prodMkproof · cited by 8
- Real.contDiffAt_rpow_of_neproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- ContDiff.rpowproof · cited by 1
- ContDiffAt.rpow_const_of_neproof · cited by 0