Re: Q. How to work with derivative?

• To: mathgroup at smc.vnet.net
• Subject: [mg6679] Re: [mg6615] Q. How to work with derivative?
• From: "Preferred Customer" <sherman.reed at worldnet.att.net>
• Date: Wed, 9 Apr 1997 09:15:58 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Clear[f,s];
f[x_]=x^3
s[x_]=D[Log[f[x]],x]
s[3]
!(x^3)(*this is output of the func def*)
!(3/x)(*this is output of the deriv*)
1       (* this is the deriv at x=3 *)

Although it is hard to read, I used your code and it executed just fine on
3.0
as well as on 2.2.3

Sherman Reed
----------
> From: Yaroslaw Bazaliy <yar at leland.stanford.edu>
To: mathgroup at smc.vnet.net
> To: mathgroup at smc.vnet.net
> Subject: [mg6679] [mg6615] Q. How to work with derivative?
> Date: Saturday, April 05, 1997 11:07 PM
>
> If any one has any experience with the following, could you please
> help?
>
> Suppose I have a function f[x], say f[x]=x^3. Then I want to calculate
> the derivative of say Log[f[x]] and evaluate it at some point, say x=3.
> I try:
> --------------------------------------
> Clear[f,s];
> f[x_]:=x^3;
> s[x_]:=D[Log[f[x]],x];
> s[3]
> General::"ivar": "\!\(3\) is not a valid variable."
> Out[47]=
> \!\(\[PartialD]\_3 Log[27]\)
> -------------------------------------
> Try onother approach:
> ------------------------------------------------
> Clear[f];
> f[x_]:=x^3;
> Function[x,D[Log[f[x]],x]][3]
> General::"ivar": "\!\(3\) is not a valid variable."
> Out[48]=
> \!\(\[PartialD]\_3 Log[27]\)
> ------------------------------------------------
> Both times my "3" goes into the notation for derivative, so
> it appears as if I want to differentiate with respect to "3".
>
> Of course I can do
> -----------------------------------------------
> Clear[f];
> f[x_]:=x^3;
> D[Log[f[x]],x]/.x->3
>
> Out[]=
> 1
> -----------------------------------------------
> and get the result, but I need a _function_ (which I can later
> plot for instanse). What is the possible way to do it along the lines
> of my first approach?
>
> Thank you for all suggestions,
> Yaroslaw.

```

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