Theorems · Theorem · real analysis
HasDerivAt.cpow_const
∀ {f : ℂ → ℂ} {f' x c : ℂ},
HasDerivAt f f' x → f x ∈ Complex.slitPlane → HasDerivAt (fun x => f x ^ c) (c * f x ^ (c - 1) * f') x- Cited by
- 5 results in Mathlib
- Foundations
- Depth 214 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Complexstatement and proof · cited by 5,565
- HasDerivAtstatement and proof · cited by 493
- Complex.slitPlanestatement and proof · cited by 113
- HasStrictDerivAt.hasDerivAtproof · cited by 52
- HasDerivAt.compproof · cited by 43
- Complex.hasStrictDerivAt_cpow_constproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- hasDerivAt_ofReal_cpow_const'proof · cited by 2
- integral_mul_cpow_one_add_sqproof · cited by 1
- Complex.partialGamma_add_oneproof · cited by 1
- Complex.betaIntegral_recurrenceproof · cited by 1
- deriv_cpow_constproof · cited by 1