早教吧 育儿知识 作业答案 考试题库 百科 知识分享

请问这道二阶求导怎么求y=tan(x+y)

题目详情
请问这道二阶求导怎么求
y=tan(x+y)
▼优质解答
答案和解析
对y=tan(x+y)求导得
y'=[sec(x+y)]^2*(1+y'),
∴y'*[cos(x+y)]^2=1+y'
-1=y'[sin(x+y)]^2,
y'=-1/[sin(x+y)]^2,
∴y''=2/[sin(x+y)]^3*cos(x+y)*(1+y')
=2/[sin(x+y)]^3*cos(x+y)*{1-1/[sin(x+y)]^2}
=-2[cos(x+y)]^3/[sin(x+y)]^5.