Theorems · Theorem · real analysis
HasDerivAt.pow
∀ {𝕜 : Type u_1} {𝔸 : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedCommRing 𝔸]
[inst_2 : NormedAlgebra 𝕜 𝔸] {f : 𝕜 → 𝔸} {f' : 𝔸} {x : 𝕜},
HasDerivAt f f' x → ∀ (n : ℕ), HasDerivAt (f ^ n) (↑n * f x ^ (n - 1) * f') x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Pow
- Cited by
- 8 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.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- one_smulproof · cited by 1,374
- NormedAlgebrastatement and proof · cited by 1,165
- HasDerivAtstatement and proof · cited by 493
- nsmul_eq_mulproof · cited by 369
- smul_applyproof · cited by 229
- NormedCommRingstatement and proof · cited by 218
- ContinuousLinearMap.toSpanSingletonproof · cited by 133
- HasDerivAt.congr_simpproof · cited by 82
- HasDerivAt.hasFDerivAtproof · cited by 27
- HasFDerivAt.hasDerivAtproof · cited by 18
Cited by8
Results whose statement or proof uses this declaration.
- monomial_has_deriv_auxproof · cited by 2
- deriv_powproof · cited by 2
- integral_cos_pow_auxproof · cited by 1
- HasDerivAt.fun_powproof · cited by 1
- Convex.taylor_approx_two_segmentproof · cited by 1
- integral_sin_pow_auxproof · cited by 1
- hasDerivAt_taylorWithinEval_succproof · cited by 1
- map_add_eq_sum_add_integral_iteratedFDerivproof · cited by 0