求y=sin^4(x/4)+cos^4(x/4)的导数 ,
问题描述：
求y=sin^4(x/4)+cos^4(x/4)的导数 ,
答
y=sin^4(x/4)+cos^4(x/4)
=sin^4(x/4)+cos^4(x/4)+2sin^2(x/4)cos^2(x/4)-2sin^2(x/4)cos^2(x/4)
=[sin^2(x/4)+cos^2(x/4)]^2 -1/2 sin^2(x/2)
=1 -1/2 sin^2(x/2)
所以
求导,得
y'=-1/2 ×2sin(x/2)×cos(x/2)×1/2
=-1/2sin(x/2)cos(x/2)
=-1/4sinx