双曲函数及其导数
双曲弦函数shx=ex−e−x2sh x = \frac {e^x-e^{-x}}{2}shx=2ex−e−x双曲余弦函数chx=ex+e−x2ch x= \frac{e^x+e^{-x}}{2}chx=2ex+e−x双曲正切函数thx=shxchxth x= \frac{sh x}{ch x}thx=chxshx双曲余切函数cothx=chxshx\coth x= \frac{ch x}
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双曲弦函数shx=ex−e−x2sh x = \frac {e^x-e^{-x}}{2}shx=2ex−e−x
双曲余弦函数chx=ex+e−x2ch x= \frac{e^x+e^{-x}}{2}chx=2ex+e−x
双曲正切函数thx=shxchxth x= \frac{sh x}{ch x}thx=chxshx
双曲余切函数cothx=chxshx\coth x= \frac{ch x}{sh x}cothx=shxchx
求导：
(shx)′=chx(sh x)' = ch x(shx)′=chx
(chx)′=shx(ch x)' = sh x(chx)′=shx
(thx)′=1ch2x(th x)' = \frac{1}{ch^2 x}(thx)′=ch2x1
(cothx)′=−1sh2x(\coth x)' =- \frac {1}{sh^2 x}(cothx)′=−sh2x1
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