y=sin(x+y)的隐函数的二阶导数.
问题描述：
y=sin(x+y)的隐函数的二阶导数.
答
y'=cos(x+y)*(1+y')
y'=-1+1/[1-cos(x+y)] ，及1+y'=1/[1-cos(x+y)]
y"= -1/[1-cos(x+y)]^2*sin(x+y)*(1+y')
=-1/[1-cos(x+y)]^2*sin(x+y)*{1/[1-cos(x+y)]}
=-sin(x+y)/[1-cos(x+y)]^3
答
y'=cos(x+y)*(1+y')y'=1/[1/cos(x+y)-1]y"= -sin(x+y)(1+y')/{cos(x+y)^2[1/cos(x+y)-1]^2}=-sin(x+y)[1+1/[1/cos(x+y)-1]/[1-cos(x+y)]^2=-sin(x+y)/[1-cos(x+y)]^3