Theorems · Theorem · real analysis
Complex.hasDerivAt_cosh
∀ (x : ℂ), HasDerivAt Complex.cosh (Complex.sinh x) x
The complex hyperbolic cosine function is everywhere differentiable, with the derivative
sinh x.
- Cited by
- 7 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.coshstatement · cited by 118
- Complex.sinhstatement · cited by 113
- HasStrictDerivAt.hasDerivAtproof · cited by 52
- Complex.hasStrictDerivAt_coshproof · cited by 4
Cited by7
Results whose statement or proof uses this declaration.
- Real.hasDerivAt_coshproof · cited by 7
- Complex.deriv_coshproof · cited by 2
- HasFDerivAt.ccoshproof · cited by 2
- HasFDerivWithinAt.ccoshproof · cited by 2
- Complex.differentiable_coshproof · cited by 1
- HasDerivAt.ccoshproof · cited by 1
- HasDerivWithinAt.ccoshproof · cited by 1