Re: Plotting a function and its derivative

*To*: mathgroup at smc.vnet.net*Subject*: [mg49557] Re: Plotting a function and its derivative*From*: Helen Read <read at math.uvm.edu>*Date*: Fri, 23 Jul 2004 05:59:58 -0400 (EDT)*Organization*: EM Computer Facility, The University of Vermont*References*: <cdljc0$85i$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

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. The problem is the delayed evaluation on d[x]. Try this: Plot[{f[x], Evaluate[d[x]]}, {x, -5, 5}] A simpler way to do it is the following. f[x_]=x^2 Plot[{f[x],f'[x]},{x,-5,5}] You might want to make them different colors while you are at it. Plot[{f[x],f'[x]},{x,-5,5},PlotStyle->{RGBColor[1,0,0],RGBColor[0,0,1]}] -- Helen Read Mathematics & Statistics University of Vermont