Theorems · Theorem · real analysis
fderiv_pow
∀ {𝕜 : Type u_1} {𝔸 : Type u_2} {E : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedCommRing 𝔸]
[inst_2 : NormedAddCommGroup E] [inst_3 : NormedAlgebra 𝕜 𝔸] [inst_4 : NormedSpace 𝕜 E] {f : E → 𝔸} {x : E} (n : ℕ),
DifferentiableAt 𝕜 f x → fderiv 𝕜 (f ^ n) x = (n • f x ^ (n - 1)) • fderiv 𝕜 f x- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Pow
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousLinearMapstatement · cited by 5,352
- NormedAlgebrastatement and proof · cited by 1,165
- DifferentiableAtstatement and proof · cited by 617
- fderivstatement · cited by 398
- NormedCommRingstatement and proof · cited by 218
- DifferentiableAt.hasFDerivAtproof · cited by 134
- HasFDerivAt.fderivproof · cited by 93
- HasFDerivAt.powproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- fderiv_fun_powproof · cited by 1