y=ln cos arctan（shx）求导
问题描述：
y=ln cos arctan（shx）求导
答
因为 dy =d [ cos arctan (sh x) ] / cos arctan (sh x)
= -[ sin arctan (sh x) ] *d [ arctan (sh x) ] / cos arctan (sh x)
= -[ tan arctan (sh x) ] *d (sh x) / [ 1 +(sh x)^2 ]
= -sh x *ch x dx / (ch x)^2
= -th x dx.
所以 dy /dx = -th x.
= = = = = = = = =
利用一阶微分形式不变性.
也可用复合函数求导法则.
微分公式：
d (ln u) =du /u,
d (cos u) =sin u du,
d (arctan u) =du /(1 +u^2),
d (sh u) =ch u du.
双曲函数：
(ch x)^2 -(sh x)^2 =1.
d (sh u) =ch u du,
d (ch u) =sh u du.
双曲函数.