求y=sin(x/2),y=(sinx)^2和y=[sin(x/2)]^2三个函数的导数?_数学解答

求y=sin(x/2),y=(sinx)^2和y=[sin(x/2)]^2三个函数的导数?

人气：317 ℃　时间：2019-10-19 22:57:04

解答

sin'(x/2)=cos(x/2)(x/2)'=cos(x/2)/2
[(sinx)^2]'=2sinx(sinx)'=2sinxcosx=sin(2x)
[sin(x/2)]^2 '=2sin(x/2)[sin(x/2)]'=2sin(x/2)cos(x/2)(x/2)'=sinx/2