Seems, like I faced 2 bugs simultaneously... From four (almost) equivalent expressions only one is calculated correctly.

1. Wrong derivative atan() with 2 arguments, shown in red.

2. Two expressions are shown in yellow, where error is reported, although the same term with dot products is successfully calculated in another expression (shown in green).

testderv.sm (14 KiB) downloaded 50 time(s).

You seem familiar with Maple.

Can't help in there, Mathcad11/Maple NOT same as Maple in Smath.
Uni reported some bugs in Maple. All CAS have bugs.

Cheers, Jean

testderv.sm (26 KiB) downloaded 50 time(s).

Wrote

You seem familiar with Maple.

Jean,

I use Maple for the first time. I found in SMath no possibility to simplify expressions (and also wrote a corresponding Feature Request). Maple plugin was the first possibility, which I found, to get readable expressions.

Both bugs here have nothing to do with Maple. To ensure that differentiation is performed by SMath, I have used Martins implementation of "symbeval()" function. Maple is used only to show differentiataion results in readable form.

testderv-sm.sm (15 KiB) downloaded 50 time(s).

The script is correct as sanity check below
but result is NOT ! as proved ... Ah !
As it looks Maple is the guilty companion.

Hello Martin, Adventurist,

Martin, one day you gave me a trick "to be more divine".
Here is one to make Maple expansion "more divine".
There is a missing link somewhere.

Jean

testderv-sm (2).sm (71 KiB) downloaded 57 time(s).