Theorems · Theorem · real analysis
HasStrictDerivAt.rpow
∀ {x : ℝ} {f g : ℝ → ℝ} {f' g' : ℝ},
HasStrictDerivAt f f' x →
HasStrictDerivAt g g' x →
0 < f x → HasStrictDerivAt (fun x => f x ^ g x) (f' * g x * f x ^ (g x - 1) + g' * f x ^ g x * Real.log (f x)) x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- TopologicalSpaceproof · cited by 24,529
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- AddCommGroupproof · cited by 12,871
- NontriviallyNormedFieldproof · cited by 8,742
- mul_commproof · cited by 2,262
- mul_assocproof · cited by 1,667
- ContinuousSMulproof · cited by 1,016
- Real.logstatement and proof · cited by 939
- smul_applyproof · cited by 229
- HasStrictDerivAtstatement and proof · cited by 163
Cited by2
Results whose statement or proof uses this declaration.
- Real.hasStrictDerivAt_const_rpowproof · cited by 3
- Real.hasStrictDerivAt_rpow_const_of_neproof · cited by 2