Re: Plotting a function and its derivative

• To: mathgroup at smc.vnet.net
• Subject: [mg49501] Re: Plotting a function and its derivative
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Thu, 22 Jul 2004 02:45:18 -0400 (EDT)
• Organization: Universitaet Leipzig
• References: <cdljc0\$85i\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

and

f[x_] := x^2; d[x_] := Block[{y}, D[ f[y], y] /. y -> x]

Plot[{f[x], d[x]}, {x, -5, 5}]

work as expected.

Regards
Jens

>
> first of all, thanks for reading this message, i would imagine this is
> a beginner level question, and sorry if this was answered previously,
> im still getting the hang of proper searches in a mathematical forum.
>
> 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_] := ¶_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
>
> anyways, to simplify my question, how to i plot a function (like x^2)
> and its derivative (like 2x) and apply its derivative to any part of
> the function (like x=3) so as to show the tangent line which should
> touch the function? i thought my way should have worked, but it seems
> the d(x) is the troublesome function, since without it, i get a graph
> of the function (albeit without the derivative).....
>
> many thanks for looking this question over!
>