Theorems · Theorem · real analysis
HasFDerivAt.const_cpow
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {f : E → ℂ} {f' : StrongDual ℂ E} {x : E}
{c : ℂ}, HasFDerivAt f f' x → c ≠ 0 ∨ f x ≠ 0 → HasFDerivAt (fun x => c ^ f x) ((c ^ f x * Complex.log c) • f') x- Cited by
- 1 results in Mathlib
- Foundations
- Depth 202 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.
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Complexstatement and proof · cited by 5,565
- StrongDualstatement and proof · cited by 459
- HasFDerivAtstatement and proof · cited by 350
- Complex.logstatement · cited by 187
- HasStrictDerivAt.hasDerivAtproof · cited by 52
- HasDerivAt.comp_hasFDerivAtproof · cited by 20
- Complex.hasStrictDerivAt_const_cpowproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- DifferentiableAt.const_cpowproof · cited by 6