Newbie question: diff,ratsimp,factor



Experimenting with maxima for the first time, I tried to compute the
derivative of (%e^x-%e^(-x))/(%e^x+%e^(-x)), which I believe should
be: 4/(e^x+e^-x)^2.

Maxima gives 1 - (e^x-e^(-x))^2/(e^x+e^(-x))^2

which is of course fine, but when I try to simplify this (I used
ratsimp(%) and then factor(%)), maxima delivers

4e^(2x)/(e^(2x)+1)^2

Perhaps this is correct, although it doesn't look like it at first
blush.

What is the best way to get the simple form of this expression?

Thanks and many apologies if this is a common question.

Scott
-- 
sdb at ssr.com
"disce quasi semper victurus 
 vive quasi cras moriturus"