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>*Reply-to*: kuska at informatik.uni-leipzig.de*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 adrian sky wrote: > > 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! > > adrian sky > > For a man to attain to an eminent degree in learning costs him time, > watching, hunger, nakedness, dizziness in the head, weakness in the > stomach, and other inconveniences. - Miguel De Cervantes