Nice explanation for our new user, but...
On 2/13/07, Daniel Lakeland <dlakelan at street-artists.org> wrote:On Tue, Feb
13, 2007 at 07:00:02AM -0000, Scott Ballantyne wrote:
>> 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....
> Stavros has given you an example of going the other way
> (complexifying a simple expression).
Be fair! The first EIGHT versions I got were shorter than his original
expression, and included the particular form he was looking for (which is in
fact the shortest form written with exponentials rather than hyperbolic
functions). Often you have to first expand (complexify) to a larger
expression before you can simplify down to the form you want....
Of course, the code for trying various simplifications could be improved in
many many ways....
-s
sech(x)^2
1/cosh(x)^2
1-tanh(x)^2
2/(cosh(2*x)+1)
{4/(%e^x+%e^-x)^2 <<<<<<<<<< form he was looking for
1-sinh(x)^2/cosh(x)^2
-(tanh(x)-1)*(tanh(x)+1)
4*%e^(2*x)/(%e^(2*x)+1)^2
1-(%e^x-%e^-x)^2/(%e^x+%e^-x)^2 <<<<<<<< Input expression