Question

高二数学，求下列函数的导数，过程越详细越好：

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

Answer 2

解 ：
y=sin^4(x/4)+cos^4(x/4)
=4sin^3(x/4)*[sin(x/4)]'+4cos^3(x/4)*[cos(x/4)]'
=4sin^3(x/4)*cos(x/4)*(x/4)'-4cos^3(x/4)*sin(x/4)*(x/4)'
=sin^3(x/4)cos(x/4)-cos^3(x/4)sin(x/4)
=sin(x/4)cos(x/4)*[sin²(x/4)-cos²(x/4)]
=(1/2)sin(x/2)*[-cos(x/2)]
=(1/4)sinx

Answer 3

y=sin^4(x/4)+cos^4(x/4)
=4sin^3(x/4)×cos(x/4)×1/4+4cos^3(x/4)×(-sin(x/4))×1/4
=sin(x/4)cos(x/4)[sin²x/4-cos²x/4]
=(sinx/2)/2×cos(x/2)
=(sinx)/2

Answer 4

怎么看不懂题目呢！