高等数学导数

1. y'=[sec(x+y)]^2(1+y')
解得 y'=-[csc(x+y)]^2 (注意一定要化简）
y''=-2csc(x+y)[-csc(x+y)cot(x+y)](1+y')
最后将y'带入化简即可。
2.dy/dt=e^y sint dy/dt+e^y cost
dy/dt=e^ycost/(1-e^ysint)
=e^ycost/(2-y)
dx/dt=6t+2
将上两式相除
dy/dx=[e^ycost/(2-y)]/(6t+2)
=e^ycost/[(2-y)(6t+2)]
d^2y/dx^2=
d{e^ycost/[(2-y)(6t+2)]}/dt dt/dx
（前面部分对t求导数，后面是t对x求导数，后面可以转化成x对t的导数的倒数，这是容易错的地方,)
(最后还要将dy/dt一阶导数带入就可以了）

1, y' = [sec(x+y)]^2 * (1+y')
=> y' = [sec(x+y)]^2/{1-[sec(x+y)]^2}

2, dy/dx = (dy/dt) / (dx/dt)
= [e^y * (dy/dx) * sint + e^y * cost] / (6t+2)

=> dy/dx = (e^y * cost) / [6t + 2 - e^y * sint]

二阶? 我不继续做了，写起来太麻烦了