differentiation - Maxima: evaluate a function f(x) embedding diff() nouns -
i generate taylor series following these instructions :
f(x) := ''(ratdisrep(taylor(qexct('x),'x,0,5)));
qexct function not defined : want perform computation qexct smooth function.
knowing this, how set variable x
value (e.g. 1) ?
if :
f(1);
then maxima returns me following error :
diff: variable must not number; found: 1
and if :
f(d);
then considers d
variable , substitutes occurrences of variable x
variable d
. in particular, differentiates using d/dd instead of d/dx. however, substitute variable x
number 1
in x^n terms , keep derivatives are…
how do ?
the variable in diff
expression not recognized everywhere in maxim dummy (formal) variable, when try evaluate f(1)
, maxima substitutes 1 diff
expression , causes error. think that's bug; i'll make bug report it.
as work around, can use add-on package pdiff
(positional derivatives) included maxima. notation little different dy/dx notation used default in maxima.
(%i1) load (pdiff) $ (%i2) f(x) := ''(ratdisrep(taylor(qexct('x),'x,0,2))); 2 qexct (0) x ""(2) (%o2) f(x) := ---------------- + qexct (0) x + qexct(0) 2 ""(1) (%i3) f(h); 2 qexct (0) h (2) (%o3) -------------- + qexct (0) h + qexct(0) 2 (1) (%i4) ev (%, qexct=sin); (%o4) h (%i5) ev (%o3, h=1); qexct (0) (2) (%o5) ----------- + qexct (0) + qexct(0) 2 (1)
i think spurious ""
in display of f(x) := ...
minor display bugs; think can ignore them.
there documentation pdiff
in share/pdiff/pdiff-doc.pdf
in maxima installation.
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