令f(x)=(),则f(n)(x)=sin(x+nπ/2),
举一反三
- 设f(x)=x(x+1)(x+2)…(x+n),则f′(0)=() A: n^2 B: (n-1)! C: n D: n!
- 已知函数f(x)具有任意阶导数,且f'(x)=[f(x)]2,则当n为大于2的正整数时,f(x)的n阶导数f(n)(x)是______. A: n![f(x)]n-1 B: n[f(x)]n+1 C: [f(x)]2n D: n![f(x)]2n
- 【单选题】5.设f 0 (x)=sinx,f 1 (x)=f 0 ′(x),f 2 (x)=f 1 ′(x),...,f n +1 (x)=f n ′(x),n∈N,则f 2011 (x)等于() A. sinx B. -sinx C. cosx D. -cosx
- 设f(x)=xx+1,定义f1(x)=f(x),f2(x)=f1(f(x)),f3(x)=f2(f(x)),…,fn(x)=fn-1(f(x)),(n≥2,n∈N)则f100(x)=1的解为x=______.
- 设函数f(x)具有任意阶导数,且f"(x)=[f(x)]2,则f(n)(x)=______ A: n![f(x)]n+1 B: n[f(x)]n+1 C: (n+1)[f(x)]n+1 D: (n+1)![f(x)]n+1