求x-y=sin(x+y)的隐函数的二阶导数,具体步骤可以有吗?
1个回答
2016-12-31
展开全部
x-y=sin(丛前x+y)
两笑段边求导:
1-y′ = cos(x+y) * (1+y′)
1 - cos(x+y) = [1+cos(x+y)]y′
y′ = [1-cos(x+y)] / [1+cos(x+y)]
= [2-1-cos(x+y)] / [1+cos(x+y)]
= 2 /渗升清 [1+cos(x+y)] - 1
两边同时求导:
y ′′ = -2sin(x+y) * (1+y′) / [1+cos(x+y)]²
= { -2sin(x+y) *2 / [1+cos(x+y)] } / [1+cos(x+y)]²
= -4sin(x+y) / [1+cos(x+y)]³
两笑段边求导:
1-y′ = cos(x+y) * (1+y′)
1 - cos(x+y) = [1+cos(x+y)]y′
y′ = [1-cos(x+y)] / [1+cos(x+y)]
= [2-1-cos(x+y)] / [1+cos(x+y)]
= 2 /渗升清 [1+cos(x+y)] - 1
两边同时求导:
y ′′ = -2sin(x+y) * (1+y′) / [1+cos(x+y)]²
= { -2sin(x+y) *2 / [1+cos(x+y)] } / [1+cos(x+y)]²
= -4sin(x+y) / [1+cos(x+y)]³
更多追问追答
追问
不过最后是正的,谢谢啊
不过最后是正的,谢谢啊
推荐律师服务:
若未解决您的问题,请您详细描述您的问题,通过百度律临进行免费专业咨询
广告 您可能关注的内容 |