Question

高数 求二阶导数

y=tan(x+y)

Answer 1

y是函数，x是自变量
两边对x求导：y'=sec^2(x+y)*(1+y')
解得：y'=sec^2(x+y)/[1-sec^2(x+y)]=-1/sin^2(x+y) (1)
两边再求导
y''=2/sin^3(x+y)*cos(x+y)*(1+y')
将（1）式代入得
y''=2/sin^3(x+y)*cos(x+y)*(1-1/sin^2(x+y))=2cos(x+y)/sin^3(x+y)-2/sin^5(x+y)

好麻烦，不知有没有算错，你再验算一下，方法肯定是对的。

Answer 2

dy/dx=1/[cos(x+y)]^2*(1+ dy/dx)=sec²(x+y)*(1+ dy/dx)
dy/dx=sec²(x+y)/[1-sec²(x+y)]=-sec²(x+y)/tan²(x+y)=-1/sin²(x+y)
二次求导
d[-1/sin²(x+y)]/dx=2/sin^3(x+y)*cos(x+y)(1+dy/dx)=2/sin^3(x+y)*cos(x+y) [1-1/sin²(x+y)]
=-2cos^3(x+y)//sin^5(x+y)

Answer 3

如图：