How to parametric plot deriv of interpolating func?

*To*: mathgroup at christensen.cybernetics.net*Subject*: [mg1564] How to parametric plot deriv of interpolating func?*From*: "Ronald J. Riegert" <riegerrj at esvax.dnet.dupont.com>*Date*: Sat, 24 Jun 1995 06:29:22 -0400*Organization*: DuPont Experimental Station, Wilmington, DE USA

I have recently started working with NDSolve and just encountered Mathematica interpolating functions for the first time. The Mathematica book says that these can be dealt with just like any other function, but I'm having difficulty using their derivatives in parametric plots. In particular, I use NDSolve to solve the second-order differential equation diffeq for x[t], and call the result soln: soln= NDSolve[{diffeq,x[0.]==0.,x'[0.]==1.},x,{t,0.,50.}][[1,1]] This gives the interpolating function: x -> InterpolatingFunction[ {0.,50.}, <>] I'm interested in plotting D[x[t],t], so I do: Plot[Evaluate[D[x[t] /. soln,t]],{t,0.,50.}] which works fine. However, I'm really want to use D[x[t],t] in a parametric plot, so I test by entering: ParametricPlot[{t, Evaluate[D[x[t] /. soln,t]]},{t,0.,50.}] which should give the same graph as the above Plot command. Instead, it produces a bunch of error messages. My question, therefore, is how do I go about using the derivative of an interpolating function in a parametric plot? Ronald J. Riegert DuPont Experimental Station riegerrj at esvax.dnet.dupont.com