求导 y=(x+cosx)/(x+sinx)

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/01 22:32:54

求导 y=(x+cosx)/(x+sinx)
求导 y=(x+cosx)/(x+sinx)

求导 y=(x+cosx)/(x+sinx)
y'=[(x+cosx)'(x+sinx)-(x+cosx)(x+sinx)']/(x+sinx)^2
=[(1-sinx)(x+sinx)-(x+cosx)(1+cosx)]/(x+sinx)^2
=[x+sinx-xsinx-(sinx)^2-x-xcosx-cosx-(cosx)^2]/(x+sinx)^2
=(sinx-cosx-xsinx-xcosx-1)/(x+sinx)^2

y导=((1-sinx)(x+sinx)-(1+cosx)(x+cosx))/(x+sinx)^2
=(sinx-cosx-xsinx-xcosx-1)/(x+sinx)^2