Finding the limit of a product as x approaches infinity

[transgalactic]

i added a link with the question and how i tried to solve it

http://img249.imageshack.us/my.php?image=img7389do6.jpg

 

[EnumaElish]

That answer is not the limit, it's what you would have gotten had you taken the derivative correctly.

To find the derivative of (1 + x)^(1/x) write Log[(1 + x)^(1/x)] = Log[1+x] / x. Say this has derivative y, which means (Log f(x))' = y = f'(x)/f(x), so f'(x) = y f(x).