Differentiating Cross

*To*: mathgroup at smc.vnet.net*Subject*: [mg66238] Differentiating Cross*From*: "Vladimir" <vladimir347 at yahoo.com>*Date*: Fri, 5 May 2006 05:02:27 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

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