Re: Q. How to work with derivative?

• To: mathgroup at smc.vnet.net
• Subject: [mg6648] Re: [mg6615] Q. How to work with derivative?
• From: Allan Hayes <hay at haystack.demon.co.uk>
• Date: Wed, 9 Apr 1997 00:34:11 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Yaroslaw Bazaliy <yar at leland.stanford.edu>
[mg6615] Q. How to work with derivative?

Writes as follows - full message appended below ********

>>>>>>>>>>>>>
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]\)
-------------------------------------
<<<<<<<<<<<

Yaroslav:

Clear[f,s];
f[x_]:=x^3;
s[x_] = D[Log[f[x]],x];  (*Set, not SetDelayed*)

s[3]
1

Allan Hayes,
hay at haystack.demon.co.uk
http://www.haystack.demon.co.uk

*************************************************
f 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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