Re: Bug in D (or Derivative) ( Was: Re: DSolve bug)

• To: mathgroup at smc.vnet.net
• Subject: [mg97930] Re: [mg97919] Bug in D (or Derivative) ( Was: Re: DSolve bug)
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Thu, 26 Mar 2009 05:19:26 -0500 (EST)
• References: <612696379.19321237704569790.JavaMail.root@mmm.inp.demokritos.gr> <200903251046.FAA24696@smc.vnet.net>

```On 25 Mar 2009, at 11:46, schochet123 at gmail.com wrote:

>
>
> The source of this bug seems to be the following bug in in D (or
> Derivative): According to Mathematica, D[u',u] yields u''. However,
> the correct answer is u''/u'
> (Homework for Calculus 1: use the chain rule to prove this.)

Not really. According to Mathematica's notion of derivative, D[u',u]
ought to be 0, since u' does not involve u explicitly. In fact,

D[u'', u']
0

which, of course, is much the same thing. The only way I know to get
the answer you have in mind with Mathematica is:

Dt[Derivative[1][u][x], u[x]]
Derivative[2][u][x]*Dt[x, u[x]]

>
>
> The way Mathematica obtains its incorrect result is quite amusing, As
> Trace shows, Mathematica evaluates D[u',u] by noting that the FullForm
> of u' is Derivative[1][u], whose derivative with respect to u is (of
> course ;) ) Derivative[1]'[u].
> Mathematica then decides that Derivative[1]'  is Derivative[2],
> yielding Derivative[2][u], i.e., u''.
>

Indeed, this is right, and has been mentioned on this forum several
times in the past (at least twice by me).
See, for example,

http://forums.wolfram.com/mathgroup/archive/2008/Jul/msg00801.html

Andrzej Kozlowski

```

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