pure , differentiation

👨🏻‍🏫 學術台數學

Green1114

2009-07-20 3:03 am

Q1 : f(x) = e^(x)x^(3).
Find f'(n)(x) for n=>3

p.s. ^(n) = power of n
f'(n) = n times differentiable

更新1:

I don't know why the Q need n>=3 ...?

更新2:

Even you'v finished the Q , could u explain a little bit about it.

回答 (1)

myisland8132

2009-07-20 3:55 am

✔ 最佳答案

Using Leibnitz Formula for the n'th Derivative of a Product
We have
f'(n)
=Σ(nCk)(e^x)(n-k)(3x^2)(k)
=Σ(nCk)(e^x)(3x^2)(k)
For n>=3, the expression is
(nC0)(e^x)(x^3)+(nC1)(e^x)(3x^2)+(nC2)(e^x)(6x)+(nC3)(e^x)(6)
=(e^x)(x^3)+3n(e^x)(x^2)+3n(n-1)(e^x)(x)+n(n-1)(n-2)(e^x)

2009-07-21 13:08:02 補充：
因為n>=4時﹐x^3的導數會是0

👍 0 👎 0

收錄日期: 2021-04-26 13:44:22
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20090719000051KK01541

檢視 Wayback Machine 備份