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Re: bug? f'[x]'
Perhaps I should have added that this: Derivative[n][Derivative[m][f]] Derivative[m + n][f] is mathematically perfectly sound, while this: Derivative[n][Derivative[m][f][x]] Derivative[m + n][f][x] cerainly is not. But this does not mean this is necesarily a bug. The syntax of second input illogical and not documented as anything meaningful in Mathematica but it returns a "meaningful answer" but perhaps might do so intentinally. Since, however, it is not documented (and illogical) it is certianly cannot be regarded as any kind of "bug". Andrzej Kozlowski > > On 28 Jul 2008, at 13:53, Benjamin.R.Lewis at gmail.com wrote: > >> G'day, >> >> In:= f'[x] =!= f[x]' && f''[x] === f'[x]' >> Out= True >> >> Can anyone explain this? >> >> -Ben >> > > Maybe not exactly explain... but > > this is a consequence of the following somewhat strange phenomenon: > > FullForm[Derivative[n][Derivative[m][f][x]]] > FullForm[Derivative[m + n][f][x]] > > but not for m=0: > > FullForm[Derivative[n][Derivative[f][x]]] > FullForm= FullForm[Derivative[n][f[x]]] > > Note that the first output is actually the (m+n)-th derivative of f > at x, but the second output means (if anything) something completely > different (n-th derivative of the functon f[x]). > > Although the first result may be part of some design, it is > mathematically just as meaningless as the second. So I would guess > the "explanation" of the phenomenon you have observed is of the > "garbage in -> garbage out" kind. > > Andrzej Kozlowski >