求由方程所确定的隐函数的导数dy/dx? y=cos(x+y)$(acontent)_数学解答

求由方程所确定的隐函数的导数dy/dx? y=cos(x+y)
$(acontent)

人气：208 ℃　时间：2019-08-19 07:34:14

解答

y=coa(x+y)
dy/dx=-sin(x+y)·(1+dy/dx)
dy/dx=-sin(x+y)-sin(x+y)·dy/dx
[1+sin(x+y)]dy/dx=-sin(x+y)
dy/dx=-sin(x+y)/[1+sin(x+y)]