y=cox(x+y)的二阶导数是

Question

y=cox(x+y)的二阶导数是

Answer 1

首先求一阶导数：
y'=-sin(x+y)(x+y)'
y'=-sin(x+y)(1+y') ====> y'=-sin(x+y)/(1+sin(x+y))
上面式子两端继续对x求导：
y''=-cos(x+y)(1+y') - sin(x+y)*y'' 乘积的求导法则
整理有 y''=-cos(x+y)(1+y') / (1+sin(x+y))
将y'代入上面式子有：
y''=-cos(x+y) / [1+sin(x+y)]