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Bypassing built-in functions in differentiation

Dear MathGroup.

consider the following statement:


which evaluates to

Dt[a] Transpose`[a]

that is, mathematica treats Transpose as a function and uses the chain
rule. i can try and bypass this behaviour manually:

Dt[Transpose[x_]] := Transpose[Dt[x]]

but now consider expressions like -


which still produces:

Transpose[a].Dt[b] + Dt[a] Transpose`[a] b

which is a bit surprising. i can of course bypass this behaviour
manually as well:

Dt[Transpose[x_].y_] := Transpose[Dt[x]].y + Transpose[x].Dt[y]

which gives the desired result, but then check the following -

etc. etc.

i tried also to define -
Dt[Transpose[x_]] =1

which produces readable results, but discards the (correct, and needed)
'Transpose' head over a factor in the differentiation.

There has to be a general solution. is there a 'hook' where i can
interfere with the derivative computation? (i thought user definitions
would suffice, but apparently not)



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