求y = (sinx/4)^4 + (cosx/4)^4导数,

来源：学生作业帮编辑：拍题作业网作业帮分类：数学作业时间：2024/04/20 09:22:49

是sin(x/4)?
y = (sin(x/4))^4 + (cos(x/4))^4
y'=4*(sin(x/4))^3*(sin(x/4))'+4*(cos(x/4))^3*(cos(x/4))'
=4*(sin(x/4))^3*cos(x/4)*1/4+4*(cos(x/4))^3*(-sin(x/4))*1/4
=(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)
=1/2*sin(x/2)*(-cos(x/2))
=-1/4*sinx
或者
y=(sin(x/4))^4 + (cos(x/4))^4
=(sin(x/4))^4 + (cos(x/4))^4+2(sin(x/4)*cos(x/4))^2-2(sin(x/4)*cos(x/4))^2
=((sin(x/4))^2+(cos(x/4))^2)^2-1/2*(sin(x/2))^2
=1-1/4*(1-cosx)
=1/4*cosx
所以
y'=-1/4*sinx

函数y=3cosx-4sinx的导数为 y=sinx-cosx ,x=π／4 求函数在给定点的导数三角函数的n阶导数设y=(sinx)^4+(cosx)^4,求y^(n) 意思是求n阶导求Y=SINX^cosX+COSX^sinX的导数求下列函数的导数：(1) y=e^x(sinx --cosx) (2) y=(1+sin2x)^4 求y=cosx/sinx的导数求y=cosx^sinx的导数求函数的奇偶性(1)y=(sinx)^4-(cosx)^4+cos2x；(2)y=1+sinx-cosx/1+sinx+ 求函数y=cosx^4的导数 y=sinx+4cosx/x 求dy/dx 求y=3sinx+4cosx最大值和最小值求y=sinx+2sinxcosx+cosx-4的值域