函数y=(x-cosx)/(x+sinx)在点x=2处的导数?

题目

函数y=(x-cosx)/(x+sinx)在点x=2处的导数?

答案

y=(x-cosx)/(x+sinx)
y=[(1+sinx)*(x+sinx)-(x-cosx)*(1+cosx)]/(x+sinx)^2
=[sinx+cosx+x(sinx-cosx)+1]/(x+sinx)^2
f(2)=[sin2+cos2+2sin2-2cos2+1]/(2+sin2)^2
=(3sin2-cos2+1)/(2+sin2)^2