simple derivative function question



On Wed, Jan 17, 2007 at 04:56:52PM -0500, sen1 at math.msu.edu wrote:

> I would like to understand the difference between the functions g(x)
> and h(x) defined below.  In particular, lines

> (%i2) h(x):= ''(diff(f(x),x));
>                                              2
> (%o2)                            h(x) := 3 x

What maxima does is read in h(x) then := then ''(diff(f(x),x)).

because of the '' the last thing is immediately evaluated at READ TIME
to 3*x^2. then h(x) is defined to be the function which takex x and
computes 3*x^2

> (%i5) g(x):= diff(f(x),x);
> (%o5)                        g(x) := diff(f(x), x)
> (%i6) g(x);
>                                          2
> (%o6)                                3 x
> (%i7) g(2);
> 
> Non-variable 2nd argument to diff:
> 2

g(x) is now defined to be the function which takes x, substitutes it
into the expressions diff(f(x),x) and then computes that derivative.

g(foo) -> diff(f(foo),foo)  -> diff(foo^3,foo) -> 3*foo^2
g(2) -> diff(f(2),2) -> diff(2^3,2) -> error

where -> could be read as "becomes"

Hope this helps.

-- 
Daniel Lakeland
dlakelan at street-artists.org
http://www.street-artists.org/~dlakelan