       Re: Re: Plotting a function and its derivative

• To: mathgroup at smc.vnet.net
• Subject: [mg49555] Re: [mg49529] Re: Plotting a function and its derivative
• From: DrBob <drbob at bigfoot.com>
• Date: Fri, 23 Jul 2004 05:59:52 -0400 (EDT)
• References: <200407220647.CAA21144@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Where Bill says DelayedSet, he means SetDelayed.

Bobby

On Thu, 22 Jul 2004 02:47:10 -0400 (EDT), Bill Rowe <readnewsciv at earthlink.net> wrote:

> On 7/21/04 at 6:40 AM, skaai at earthlink.net (adrian sky) wrote:
>
>> anyways, what i'm trying to do is illustrate the simplest of
>> derivatives in the form of a graph but i am getting errors.
>
>> the function i'm trying to derive is x^2 its derivative i'm trying
>> to illustrate is 2x
>
>> i would like to set up a graph which allows me to determine the
>> argument (be it x^2 or x^4+1), calculate its derivative, and graph
>> them so as to illustrate their relationship.
>
>> i know that the derivative can be graphed at any x value, and as
>> far as this is concerned, the value can be anything, probably a
>> small value to keep the graph manageable.
>
>> anyways, i'm inputting this: f[x_] := x^2; d[x_] := Ã¢Ë?â??_x f[x] which
>> supposedly should assign the f(x) a value of ^2 and d(x) a value of
>> the derivative of f(x)
>
>> i can even type f(x) and get back the value x^2 and d(x) gives me
>> 2x, so it seems the system understands and assigns the requested
>> values
>
>> but when I try to plot this with the command: Plot[{f[x], d[x]},
>> {x, -5, 5}] i get numerous errors and only get the graph of x^2 the
>> errors are: General::ivar: -5. is not a valid variable. Plot::plnr:
>> d[x] is not a machine-size real number at x = -4.9999995833333335`
>> Plot::plnr: d[x] is not a machine-size real number at x =
>> -4.594330084270842` and a few more similar plot errors
>
> The problem you are having is due to the way Plot evaluates its arguements. What is happening is Plot sends your function d a numeric value and d attempts to take the derivative of a numeric value with respect to x. This is clearly not what you want.
>
> There are two ways around this. First, you can define d using Set rather than DelayedSet. That will cause the derviative to be evaluated before Plot tries to substitute a value for x.
>
> The second way would be to use Evaluate to force evaluation of the derivative before Plot substitutes values for x, i.e., with your d defined as is do:
>
> Plot[Evaluate@{f[x],d[x]}, {x, -5, 5}]
>
> Look at the discussion of Plot, Set and DelayedSet in the Mathematica Book for a more complete discussion.
> --
> To reply via email subtract one hundred and four
>
>
>

--
DrBob at bigfoot.com
www.eclecticdreams.net

```

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