求下列函数的导数,y=sin^4四分之x+cos^4四分之x

Question

求下列函数的导数,
y=sin^4四分之x+cos^4四分之x

Answer 1

易知
y={[sin(x/4)]²+[cos(x/4)]²}²-2sin²(x/4)cos²(x/4)
=1-(1/2)[sin(x/2)]²
∴y=1-(1/2)[sin(x/2)]²
求导,
y'=-(1/2)×2[sin(x/2)]×[cos(x/2)]×(1/2)
=-(1/4)sinx
∴y'=-(sinx)/4