y0=nso.v+Cn91.v'+Cn4.v"+.+C5”.v》+C'v+Mv0 =C4+C8-9+0 50.492-2sin2r+50-2r249cos2x+x2(-250sin20 2 sin2r+50xcos2x+1225sin2x). 11.求下列函数的n阶导数的一般表达式： (1)y=x”+ax1+a,x-2+.+an-x+an(a,a2,.,a都是常数0： (2)y=sin'x:(3)y=xInx: (4)y=xe' 解：(1)y'=m+(n-I)ax"2+(n-2)ax3+.+a- y'=nn-10.x-2+(n-ln-2)a,x-3+(n-2n-3)a,x-3+.+2an-2 . ym=nn-10x-2+(m-10n-2n-3).21=nl. (2)v'=2sin xcosx=sin 2x, y"=2cos2x=2sin(2x+) y"=22cos(2r+)=2sin(2r+2 4=2c0s2x+2)=2sin(2x+3受) =2-1sin[2r+0u-0. (3)y=nx+1, y.d y"=-x2=(-1)x2, y4=(-10(-2)x3, =(←-2-3.（←n+2x(r024-(ra2