Theorems · Theorem · real analysis
Complex.hasStrictDerivAt_cosh
∀ (x : ℂ), HasStrictDerivAt Complex.cosh (Complex.sinh x) x
The complex hyperbolic cosine function is everywhere strictly differentiable, with the
derivative sinh x.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Moduleproof · cited by 20,661
- AddCommGroupproof · cited by 12,871
- NontriviallyNormedFieldproof · cited by 8,742
- Complexstatement and proof · cited by 5,565
- sub_eq_add_negproof · cited by 1,023
- ContinuousSMulproof · cited by 1,016
- div_eq_mul_invproof · cited by 715
- Complex.expproof · cited by 612
- HasStrictDerivAtstatement and proof · cited by 163
- Complex.coshstatement and proof · cited by 118
- Complex.sinhstatement and proof · cited by 113
Cited by4
Results whose statement or proof uses this declaration.
- Complex.hasDerivAt_coshproof · cited by 7
- Real.hasStrictDerivAt_coshproof · cited by 3
- HasStrictFDerivAt.ccoshproof · cited by 0
- HasStrictDerivAt.ccoshproof · cited by 0