双曲弦函数 s h x = e x − e − x 2 sh x = \frac {e^x-e^{-x}}{2} shx=2ex−e−x
双曲余弦函数 c h x = e x + e − x 2 ch x= \frac{e^x+e^{-x}}{2} chx=2ex+e−x
双曲正切函数 t h x = s h x c h x th x= \frac{sh x}{ch x} thx=chxshx
双曲余切函数 coth x = c h x s h x \coth x= \frac{ch x}{sh x} cothx=shxchx
求导：
s h x ) ′ = c h x sh x)’ = ch x shx)′=chx
c h x ) ′ = s h x ch x)’ = sh x chx)′=shx
t h x ) ′ = 1 c h 2 x th x)’ = \frac{1}{ch^2 x} thx)′=ch2x1
coth x ) ′ = 1 s h 2 x \coth x)’ = \frac {1}{sh^2 x} cothx)′=sh2x1