Theorems · Theorem · special functions
Complex.hasDerivAt_exp
∀ (x : ℂ), HasDerivAt Complex.exp (Complex.exp x) x
The complex exponential is everywhere differentiable, with the derivative exp x.
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Complexstatement and proof · cited by 5,565
- Norm.normproof · cited by 5,413
- LT.lt.leproof · cited by 2,189
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- Complex.expstatement and proof · cited by 612
- zero_lt_oneproof · cited by 598
- HasDerivAtstatement · cited by 493
- dist_zero_rightproof · cited by 172
- norm_powproof · cited by 106
- Metric.ball_mem_nhdsproof · cited by 64
- Asymptotics.IsBigO.trans_isLittleOproof · cited by 32
Cited by10
Results whose statement or proof uses this declaration.
- Real.hasDerivAt_expproof · cited by 10
- Complex.hasStrictDerivAt_expproof · cited by 8
- HasDerivAt.cexpproof · cited by 4
- Complex.differentiable_expproof · cited by 4
- HasFDerivWithinAt.cexpproof · cited by 2
- integral_exp_mul_complexproof · cited by 2
- hasDerivAt_fourierproof · cited by 2
- Complex.deriv_expproof · cited by 2
- HasDerivWithinAt.cexpproof · cited by 1
- Complex.contDiffAt_logproof · cited by 0