2016新课标名师导学新高考第一轮总复习(文科数学)同步测试卷推理(3)

2.设 f0(x)=sin x,f1(x)=f0′(x),f2(x)= f′1(x), ,fn(x)=f′n-1(x)(n∈N),则 f2 015(x)等于 (D ) A.sin x B.-sin x C.cos x D.-cos x 【解析】由题意可知 f1(x)=(sin x)′=cos x, f2(x)=(cos x)′=-sin x, f3(x)=(-sin x)′=-cos x, f4(x)=(-cos x)′=sin x, f5(x)=(sin x)′=cos x=f1(x), f6(x)=(cos x)′=-sin x=f2(x),