Theorems · Theorem · special functions
DifferentiableAt.cexp
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAlgebra 𝕜 ℂ] {E : Type u_2}
[inst_2 : NormedAddCommGroup E] [inst_3 : NormedSpace 𝕜 E] {f : E → ℂ} {x : E},
DifferentiableAt 𝕜 f x → DifferentiableAt 𝕜 (fun x => Complex.exp (f x)) x- Cited by
- 4 results in Mathlib
- Foundations
- Depth 171 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.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Complexstatement and proof · cited by 5,565
- NormedAlgebrastatement and proof · cited by 1,165
- DifferentiableAtstatement and proof · cited by 617
- Complex.expstatement · cited by 612
- DifferentiableAt.hasFDerivAtproof · cited by 134
- HasFDerivAt.differentiableAtproof · cited by 83
- HasFDerivAt.cexpproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Differentiable.cexpproof · cited by 4
- ModularForm.logDeriv_qParamproof · cited by 1
- jacobiTheta₂'_functional_equationproof · cited by 1
- ModularForm.logDeriv_one_sub_mul_cexp_compproof · cited by 0