y=sin(x+y)的隐函数的二阶导数.

题目

y=sin(x+y)的隐函数的二阶导数.

答案

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