Theorems · Theorem · real analysis
hasDerivAt_ofReal_cpow_const
∀ {x : ℝ}, x ≠ 0 → ∀ {r : ℂ}, r ≠ 0 → HasDerivAt (fun y => ↑y ^ r) (r * ↑x ^ (r - 1)) xAn alternate formulation of hasDerivAt_ofReal_cpow_const'.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 216 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Complex.ofRealstatement and proof · cited by 1,654
- HasDerivAtstatement and proof · cited by 493
- sub_add_cancelproof · cited by 344
- HasDerivAt.congr_simpproof · cited by 82
- mul_div_cancel₀proof · cited by 77
- HasDerivAt.const_mulproof · cited by 25
- sub_eq_neg_selfproof · cited by 2
- hasDerivAt_ofReal_cpow_const'proof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Complex.deriv_ofReal_cpow_constproof · cited by 2
- DifferentiableAt.ofReal_cpow_constproof · cited by 0