arcsech
arcsech is the inverse function of the hyperbolic secant, sech(y) = 1 / cosh(y). Since cosh(y) ≥ 1 for all real y, sech(y) takes values in (0, 1], making arcsech defined on the real interval (0, 1], with arcsech(1) = 0 and arcsech(x) → ∞ as x → 0+.
For real x in (0, 1], arcsech x can be expressed as arcsech x = arcosh(1/x). A convenient
Derivative properties: on 0 < x < 1, d/dx arcsech x = −1 / (x sqrt(1 − x^2)). This derivative mirrors
Domain, range, and behavior: the real domain of arcsech is 0 < x ≤ 1, with arcsech(1) = 0.
Relationships and usage: arcsech is the inverse of sech when restricted to nonnegative arguments, so for y
Extensions to complex arguments exist and require branch choices, but the above describes the standard real-valued