y=tan（x+y）二阶导数
问题描述：
y=tan（x+y）二阶导数
答
y=tan(x+y)
两边同时对x进行求导：y'=sec²(x+y)×(1+y')
[1-sec²(x+y)]y'=sec²(x+y)
-tan²(x+y)y'=sec²(x+y)
y'=-1/sin²(x+y)
两边同时对x进行求导：y''=-2×[sin(x+y)]^(-3)×cos(x+y)×(1+y')
=-2×[sin(x+y)]^(-3)×cos(x+y)×[1-1/sin²(x+y)]
=2cos³(x+y)/[sin(x+y)]^5
答
y'= dy/dx =sec^2（x+y)·(1+y');→[sec^2（x+y) -1]·y'=sec^2（x+y);→[tan^2（x+y) ]·y'=sec^2（x+y);→y'=1/sin^2（x+y);则:y'' =dy' /dx=d[sin^(-2)（x+y)] /dx=(-2)·sin^(-3)（x+y) ·cos（x+y)·(1+y') =－...