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Theorems · Theorem · real analysis

HasDerivAt.rpow

∀ {f g : ℝ → ℝ} {f' g' x : ℝ},
  HasDerivAt f f' x →
    HasDerivAt g g' x →
      0 < f x → HasDerivAt (fun x => f x ^ g x) (f' * g x * f x ^ (g x - 1) + g' * f x ^ g x * Real.log (f x)) x
Defined in
Mathlib.Analysis.SpecialFunctions.Pow.Deriv
Cited by
1 results in Mathlib
Foundations
Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Real.hasDerivAt_Gamma_one_half · cited by 1Real.hasDerivAt_Gamma_one…Real · cited by 25697RealReal.log · cited by 939Real.logHasDerivAt · cited by 493HasDerivAthasDerivWithinAt_univ · cited by 18hasDerivWithinAt_univHasDerivWithinAt.rpow · cited by 2HasDerivWithinAt.rpowHasDerivAt.rpowCITED BYCITES

Cites5

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Cited by1

Results whose statement or proof uses this declaration.