Limits behave incorrectly when applied to derivatives

Imported from SourceForge on 2024-07-08 09:36:34 Created by pbruin on 2015-01-07 10:25:46 Original: https://sourceforge.net/p/maxima/bugs/2877

The following example exhibits two (possibly related) problems in combining limits with derivatives:

(%i1) dg: diff(g(x), x);
                                   d
(%o1)                              -- (g(x))
                                   dx
(%i2) lim: limit(dg, x, 0);
                                      d
(%o2)                          limit  -- (g(x))
                               x -> 0 dx
(%i3) limit(lim, x, 0);
                                          d
(%o3)                      limit  (limit  -- (g(x)))
                           x -> 0  x -> 0 dx
(%i4) limit(lim, a, 0);
                                   d
(%o4)                              -- (g(x))
                                   dx

in %o3, the double limit over x is not simplified;
in %o4, taking the limit over a (which does not appear in the expression) makes the limit over x disappear.

Maxima version: branch_5_35_base_65_g7a1bf8c The above happens with both GCL and ECL.

rtoy / maxima

Limits behave incorrectly when applied to derivatives #3600