已知f(x)=xex,定义f1(x)=f′(x),f2(x)=[f1(x)]′,…,fn+1(x)=[fn(x)]′,n∈N*.经计

2025-06-21 21:23:46
推荐回答(1个)
回答1:

∵f1(x)=

1?x
ex
=
(?1)1(x?1)
ex

f2(x)=
x?2
ex
=
(?1)2(x?2)
ex

f3(x)=
3?x
ex
=
(?1)3(x?3)
ex

…,
由此归纳可得:fn(x)=
(?1)n(x?n)
ex

故答案为:
(?1)n(x?n)
ex