Theorems · Theorem · real analysis
HasStrictFDerivAt.log
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : E → ℝ} {x : E} {f' : StrongDual ℝ E},
HasStrictFDerivAt f f' x → f x ≠ 0 → HasStrictFDerivAt (fun x => Real.log (f x)) ((f x)⁻¹ • f') x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 203 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
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Real.logstatement · cited by 939
- StrongDualstatement and proof · cited by 459
- HasStrictFDerivAtstatement and proof · cited by 261
- HasStrictDerivAt.comp_hasStrictFDerivAtproof · cited by 19
- Real.hasStrictDerivAt_logproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Real.hasStrictFDerivAt_rpow_of_posproof · cited by 4
- Real.hasStrictFDerivAt_rpow_of_negproof · cited by 2