Theorems · Theorem · real analysis
Complex.hasDerivAt_cos
∀ (x : ℂ), HasDerivAt Complex.cos (-Complex.sin x) x
The complex cosine function is everywhere differentiable, with the derivative -sin x.
- Cited by
- 10 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.
Cites6
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
- HasDerivAtstatement · cited by 493
- Complex.cosstatement · cited by 279
- Complex.sinstatement · cited by 258
- HasStrictDerivAt.hasDerivAtproof · cited by 52
- Complex.hasStrictDerivAt_cosproof · cited by 5
Cited by10
Results whose statement or proof uses this declaration.
- Real.hasDerivAt_cosproof · cited by 12
- Complex.tendsto_norm_tan_of_cos_eq_zeroproof · cited by 3
- HasFDerivAt.ccosproof · cited by 2
- HasFDerivWithinAt.ccosproof · cited by 2
- HasDerivAt.ccosproof · cited by 1
- EulerSine.antideriv_sin_comp_const_mulproof · cited by 1
- EulerSine.integral_sin_mul_sin_mul_cos_pow_eqproof · cited by 1
- HasDerivWithinAt.ccosproof · cited by 1
- Complex.deriv_cosproof · cited by 1
- Complex.differentiable_cosproof · cited by 1