Mathlib Map

Theorems · Theorem · real analysis

HasDerivAt.rpow_const

∀ {f : ℝ → ℝ} {f' x p : ℝ},
  HasDerivAt f f' x → f x ≠ 0 ∨ 1 ≤ p → HasDerivAt (fun y => f y ^ p) (f' * p * f x ^ (p - 1)) x
Defined in
Mathlib.Analysis.SpecialFunctions.Pow.Deriv
Cited by
2 results in Mathlib
Foundations
Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

integrableOn_add_rpow_Ioi_of_lt · cited by 1integrableOn_add_rpow_Ioi…deriv_rpow_const · cited by 0deriv_rpow_constReal · cited by 25697RealHasDerivAt · cited by 493HasDerivAthasDerivWithinAt_univ · cited by 18hasDerivWithinAt_univHasDerivWithinAt.rpow_const · cited by 2HasDerivWithinAt.rpow_con…HasDerivAt.rpow_constCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.