Plotting a function and its derivative

*To*: mathgroup at smc.vnet.net*Subject*: [mg49478] Plotting a function and its derivative*From*: adrian sky <skaai at earthlink.net>*Date*: Wed, 21 Jul 2004 06:40:27 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

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