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 >

**References**:**Re: Delayed Derivative Operator***From:*DrMajorBob <drmajorbob@bigfoot.com>