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differentiation of cross products

  • To: mathgroup at smc.vnet.net
  • Subject: [mg16419] differentiation of cross products
  • From: "Issac Trotts" <trotts at ucdavis.edu>
  • Date: Sat, 13 Mar 1999 02:21:37 -0500
  • Sender: owner-wri-mathgroup at wolfram.com

Can anyone tell me how to differentiate the cross product
of two vector-valued functions in Mathematica?
The input

D[Cross[g[t],h[t]],t]

results in the output

h'[t] Cross^(0,1)[g[t], h[t]] + g'[t] Cross^(1,0)[g[t], h[t]]

which is not correct.  The correct answer would be

Cross[g'[t], h[t]] + Cross[g[t], h'[t]]

I also tried

(Cross[g[#],h[#]]&)'

which gave me the following incorrect output:

Cross^(1,0)[g[#1], h[#1]] g'[#1] + Cross^(0,1)[g[#1], h[#1]] h'[#1] &

Please tell me if you know of a good way to deal with
this problem.

Thanks,
Issac Trotts

P.S.: Please send your response to trotts at ucdavis.edu .






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