y=sin^4 x/4 + cos^4 x/4 求导数 …………

题目

y=sin^4 x/4 + cos^4 x/4 求导数 …………

答案

y=sin^4 x/4 + cos^4 x/4
y'=4sin^3(x/4)*cos(x/4)*(1/4)+4cos^3(x/4)*(-sinx/4)*(1/4)
=sin^3(x/4)cos(x/4)-cos^3(x/3)sin(x/4)
=sin(x/4)cos(x/4)[sin^2(x/4)-cos^2(x/4)]
=(sinx/2)/2 * (-cosx/2)
=(-sinx)/4
y=(sin^4 x/4 + cos^4 x/4)
=(sin^2(x/4)+cos^2(x/4))²-2sin^2(x/4)cos^2(x/4)
=1-2sin^2(x/4)cos^2(x/4)
=1-(1/2)(sinx/2)²
求导
y=-1/2 * 2(sinx/2) *cos(x/2) *(1/2)
=(-1/4)sinx