> How can I write function as result of formula?
>
> if i try :
> f(x):=diff(sin(x),x);
>
> it gives no result ...
I am not sure exactly what you want to do, but I will guess that you
expect f(x):=... to define a *mathematical* function which you can then
manipulate formally. That is not the way Maxima works. Maxima normally
manipulates *expressions*, not named functions.
Probably what you want to do is something like:
f: diff(sin(x),x);
That now sets the programming variable f to the *expression* cos(x).
Named mathematical functions like f(x) are useful in Maxima primarily
when they are *not* defined, and you want to manipulate them formally,
e.g.
expr: log(f(x)/(f(x)+1))$
diff(expr,x)
=> (f(x)+1)*
('diff(f(x),x,1)/(f(x)+1)-f(x)*'diff(f(x),x,1)/(f(x)+1)^2)
/f(x)
ratsimp(%)
=> 'diff(f(x),x,1)/(f(x)^2+f(x))
subst(sin,f,%)
=> 'diff(sin(x),x,1)/(sin(x)^2+sin(x))
%,diff;
/* carry out the differentiation */
=> cos(x)/(sin(x)^2+sin(x))
I hope this is helpful. Please feel free to ask more questions about
this or other issues.
-s