pure (higher derivatives)

As follows:

圖片參考：http://i707.photobucket.com/albums/ww74/stevieg90/08-16.jpg


2010-02-18 20:11:03 補充：
By the way, can you tell me the reason why you delete my previous answer?

2010-02-18 20:26:02 補充：
http://i707.photobucket.com/albums/ww74/stevieg90/08-16.jpg

when n=0 , y=(-1)^0(x-0)e^(-x) , it is true for n=0

Assume it is true for n = k , where k is a non-negative integer ,

i.e. d^ky/dx^k=(-1)^(k)(x-k)e^(-x)

Consider n=k+1 ,

d^(k+1)y/dx^(k+1)

=d(d^ky/dx^k)/dx

=(-1)^k ( e^(-x)-(x-k)e^(-x)

=(-1)^(k+1)(x-(k+1))e^(-x)

it is true for n=k+1

By mathematical induction , it is true for all non- negative integer n.

2010-02-18 20:15:56 補充：
快我一步 .... so sad