设y=y(x)是由方程cos(x+y)+y=1所确定的函数,求导数dy/dx

问题描述:

设y=y(x)是由方程cos(x+y)+y=1所确定的函数,求导数dy/dx

cos(x+y)+y=1 两边同时对x求导
-(1+y~)sin(x+y)+y~=0
可得:
=(1+y~)sin(x+y)
=sin(x+y)/(1-sin(x+y))