f(x)=(ax+b)sinx+(cx+d)cosx,确定a,b,c,d,使f(x)求导=xcosx

f(x)=axsinx+bsinx+cxcosx+dcosxf(x)求导=a(sinx+xcosx)+bcosx+c(cosx-xsinx)-dsinx=(a-d)sinx+(b+c)cosx+axcosx-cxsinx因为f(x)求导=xcosx所以,得方程组a-d=0,b+c=0,a=1,c=0解得,a=1,b=0,c=0,d=1