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Differentiating Cross


Hello!

We have a handy default rule for Dot:

In[]:= Dt[a . b, t]

Out[]= a . Dt[b, t] + Dt[a, t] . b


So I'd like to have a similar behavior for Cross,
but it looks like chain rule is used instead:

In[]:= Dt[Cross[a, b], t]

Out[]= Dt[b, t]*Derivative[0, 1][Cross][a, b] +
          Dt[a, t]*Derivative[1, 0][Cross][a, b]


So I defined required transformation:

In[]:= Unprotect[Dt];
Dt[Cross[a_, b_], t_] := Cross[a, Dt[b, t]] + Cross[Dt[a, t], b];

which works for just Dt[Cross[a, b], t],
but it still doesn't work when Cross is a part
of expression like Dt[Cross[a, b] + c, t] etc.

What am I doing wrong?

--
Vladimir


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