导数运算

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

在求导前应该考虑一下对三角形的化简。

y'=(sin(x/4))^3*cos(x/4)-(cos(x/4))^3*sin(x/4)
就是利用分步求导就行了

y=(sin(x/4))^4+(cos(x/4))^4
y'=4(sin(x/4))^4+(cos(x/4))^3*(4sin(x/4)^3*cos(x/4)*(1/4)-sin(x/4)*(1/4))
y'=4(sin(x/4))^4+(cos(x/4))^3*(sin(x/4)^3*cos(x/4)-sin(x/4)*(1/4))

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

y'=(sin(x/4))^3*cos(x/4)-(cos(x/4))^3*sin(x/4)
=sin(x/4)cos(x/4){sin*(x/4)^2-cos(x/4)^2}
=-sin(x/4)cos(x/4)cos(x/2)
=-1/2*sin(x/2)cos(x/2)
=-1/4*sin(x)

y=(sin(x/4))^4+(cos(x/4))^4
y'=(sin(x/4))^3*cos(x/4)-(cos(x/4))^3*sin(x/4)
=sin