Re: Re: Delayed Derivative Operator

• To: mathgroup at smc.vnet.net
• Subject: [mg81846] Re: [mg81785] Re: [mg81762] Delayed Derivative Operator
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Thu, 4 Oct 2007 04:37:10 -0400 (EDT)
• References: <17850401.1191395290047.JavaMail.root@m35> <200710031008.GAA20090@smc.vnet.net>

```On 3 Oct 2007, at 19:08, DrMajorBob wrote:

> For f'[x] to be defined, you first have to define f[x] -- and even
> then
> Mathematica may not "know" what f'[x] should be. These are fine:
>
> f[x_] = x^3;
> f'[x]
>
> 3 x^2
>
> f[x_] := x^3
> f'[x]
>
> 3 x^2
>
> Clear[f]
> f[x_] := If[x <= 0, x^3, x^-3]
> f'[x]
>
> If[x <= 0, 3 x^2, -(3/x^4)]
>
> but this isn't quite so helpful:
>
> Clear[f]
> f[x_]/;x<=0:=x^3
> f[x_]/;x>0:=x^-3
> f'[x]
>
> f'[x]
>
> We take what we can get.

Indeed. That's one of the reasons why we have got Piecewise:

Clear[f]
f[x_] := Piecewise[{{x^3, x > 0}, {x^(-3), x < 0}}]

f'[x]

Piecewise[{{-(3/x^4), x < 0}, {3*x^2, x > 0}}, Indeterminate]

Andrzej Kozlowski

>
> Bobby
>
> On Wed, 03 Oct 2007 01:26:48 -0500, ToddSmith <elliptic1 at gmail.com>
> wrote:
>
>> Hi,
>>  I would like to be able to have an equation
>>
>> eq := D[f[x],x]==5;
>>
>> And a substitution rule
>>
>> rule = f[x]->x^3;
>>
>> And perform the substitution
>>
>> eq/.rule
>>
>> And get back the equation 3x^2==5. But Mathematica sees f'[x] and
>> doesn't do any substitutions. I tried a delayed assignment for eq but
>> it didn't work. What can I do?
>>
>> -Thanks
>>
>>
>>
>
>
>
> --
>
> DrMajorBob at bigfoot.com
>

```

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