设f(x)=(ax+b)sinx+(cx+d)cosx,试确定常数a,b,c,d,使得f′(x)=xcosx.

问题描述:

设f(x)=(ax+b)sinx+(cx+d)cosx,试确定常数a,b,c,d,使得f′(x)=xcosx.

由已知f′(x)=[(ax+b)sinx+(cx+d)cosx]′=[(ax+b)sinx]′+[(cx+d)cosx]′=(ax+b)′sinx+(ax+b)(sinx)′+(cx+d)′cosx+(cx+d)•(cosx)′=asinx+(ax+b)cosx+ccosx-(cx+d)sinx=(a-cx-d)sin...