Re: bug? f'[x]'

*To*: mathgroup at smc.vnet.net*Subject*: [mg90933] Re: bug? f'[x]'*From*: Ben <Benjamin.R.Lewis at gmail.com>*Date*: Wed, 30 Jul 2008 03:52:47 -0400 (EDT)*References*: <200807281153.HAA20595@smc.vnet.net> <344EC9C4-D0D2-4141-855E-DBE283AA7586@mimuw.edu.pl>

Mathematica does distinguish between f'[x] (evaluating the derivative) and f[x]' (derivative of the evaluation), so it seems unreasonable that this behaviour should change when f is written in terms of its antiderivative (i.e., f->g'). In other words, what is the justification for Derivative[i] [ (Derivative[j][g][x]) ][y] ever evaluating to Derivative[i+j][g][x] [y]? Even this behaviour is not consistent. Mathematica reverts to mathematically correct behaviour again if g was explicitly specified. For example, consider the function that takes an argument and returns the operator for multiplication by the cube of that argument (g=Function[x,Function[y,y*x^3]]). The derivative of its evaluation is obviously (an operator that returns) a constant (namely the cube of that argument, or zero for higher derivatives). By contrast, the evaluation of the derivative is not a constant (it is the partial with respect to the argument, an operator for multiplication by thrice the squared argument; zero is not produced until the fourth derivative). So, {g''[x][y],g'[x]'[y],g[x]''[y]}==={6xy,3x^2,0}. Even Derivative[j]//Derivative[i] evaluates further, nonsensically (garbage input ought only echo), as though a rule constraint had been overlooked. I wondered if there could be scoping error, as internal conversions involving #& are documented for Derivative. Also, this is not the only case of odd behaviour involving the distinction between numbers and operators: http://groups.google.com/group/comp.soft-sys.math.mathematica/browse_thread/thread/2b99d45979de6fd9/06396fcccf718c01 Ben On Jul 29, 3:48 pm, Andrzej Kozlowski <a... at mimuw.edu.pl> wrote: > Since, however, it is not documented > (and illogical) it is certianly cannot be regarded as any kind of "bug".

**Follow-Ups**:**Re: Re: bug? f'[x]'***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

**References**:**bug? f'[x]'***From:*Benjamin.R.Lewis@gmail.com