Theorems · Theorem · real analysis
deriv_pow
∀ {𝕜 : Type u_1} {𝔸 : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedCommRing 𝔸]
[inst_2 : NormedAlgebra 𝕜 𝔸] {f : 𝕜 → 𝔸} {x : 𝕜},
DifferentiableAt 𝕜 f x → ∀ (n : ℕ), deriv (f ^ n) x = ↑n * f x ^ (n - 1) * deriv f x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Pow
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- NormedAlgebrastatement and proof · cited by 1,165
- derivstatement · cited by 676
- DifferentiableAtstatement and proof · cited by 617
- NormedCommRingstatement and proof · cited by 218
- HasDerivAt.derivproof · cited by 147
- DifferentiableAt.hasDerivAtproof · cited by 114
- HasDerivAt.powproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- deriv_fun_powproof · cited by 9
- Derivative.normalizedDerivOfComplex_powproof · cited by 0