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I would like to work with the command Dot assuming symmetry. Specifically with the order

D[v[t].v[t], t] I get the following output

v[t].v'[t] + v'[t].v[t].

But I would like to get this one

2 v[t].v'[t]

Thanks in advice.

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    $\begingroup$ The simplest way to achieve this would be SetAttributes[Dot, Orderless]. You can remove the Orderless attribute afterwards with ClearAttributes[Dot, Orderless]. See also Carl Woll's answer here: mathematica.stackexchange.com/a/155396/72682 if you don't want to change attributes: $Assumptions = (v[t] | v'[t]) \[Element] Vectors[2]; TensorReduce[D[v[t].v[t], t]] $\endgroup$
    – flinty
    Sep 23 '20 at 11:19

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