#2877 Limits behave incorrectly when applied to derivatives

[Peter Bruin]

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.

[Barton Willis]

Bug still present in 5.47.