求下列函数的导数(1)y=sin∧4(x/4)+cos∧4 (x/4)(2)y=㏑x/x

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/04 07:41:57
求下列函数的导数(1)y=sin∧4(x/4)+cos∧4 (x/4)(2)y=㏑x/x

求下列函数的导数(1)y=sin∧4(x/4)+cos∧4 (x/4)(2)y=㏑x/x
求下列函数的导数(1)y=sin∧4(x/4)+cos∧4 (x/4)(2)y=㏑x/x

求下列函数的导数(1)y=sin∧4(x/4)+cos∧4 (x/4)(2)y=㏑x/x
1)y=Y=4sin3(x/4)*cos(x/4)*1/4+4cos3(x/4)*(-sin(x/4))*1/4
=sin(x/4)cos(x/4)(sin2(x/4)+cos2(x/4))
=sin(x/4)cos(x/4)
2)Y=(x*1/x-1*lnX)/x2
=(1-lnX)/X2

1)
y'=4sin³(x/4)/4=sin³(x/4)
2)
y'=[(1/x)x-lnx]/x²=(1-lnx)/x²你这一看就知道是错的...看错题了 1)y=sin∧4(x/4)+cos∧4 (x/4) y'=4sin³(x/4)cos(x/4)/4 +4cos³(x/4)sin(x/4)/4 =si...

全部展开

1)
y'=4sin³(x/4)/4=sin³(x/4)
2)
y'=[(1/x)x-lnx]/x²=(1-lnx)/x²

收起

(1)y'=(1/4)*cosx/4*4(sinx/4)^3-(1/4)sinx/4*4(cosx/4)^3
=sinx/4cosx/4[(sinx/4)^2-(cosx/4)^2]
=-(1/2)sinx/2cosx/2
=-(1/4)sinx
(2)y'=[(lnx)'*x-(lnx)*x']/x^2=(1-lnx)/x^2

1. y=sinx
2.(1-lnx)/x^2