y=-sin(x/2)(1-2(cosx/4)^2)的导数

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y=-sin(x/2)(1-2(cosx/4)^2)的导数y=-sin(x/2)(1-2(cosx/4)^2)的导数y=-sin(x/2)(1-2(cosx/4)^2)的导数先化简再求导数:∵y=-s

y=-sin(x/2)(1-2(cosx/4)^2)的导数
y=-sin(x/2)(1-2(cosx/4)^2)的导数

y=-sin(x/2)(1-2(cosx/4)^2)的导数
先化简再求导数:
∵y=-sin(x/2)(1-2(cosx/4)^2
=-sin(x/2)[1-(1+cos(x/2))]
=-sin(x/2)[-cos(x/2)]
=sin(x/2)*cos(x/2)
=sinx/2
∴y′=cosx/2.

3/2*cos(1/2*x), 希望能够帮助你,,~~

y’=-cos(x/2){1-2[cos(x/4)]^2}-sin(x/2)·{0-2·2cos(x/4)·[-sin(x/4)]·(1/4)}=-cos(x/2)·[-cos(x/2)]-sin(x/2)·cos(x/4)·sin(x/4)=cos(x/2)^2-(1/2)·sin(x/2)·sin(x/2)=cos(x/2)^2-(1/2)sin(x/2)^2

y=-sin(x/2)[-cos(x/2)]
=1/2 sinx
y'=1/2 cosx