plotting the derivative of a splined/interpolated function

• To: mathgroup at smc.vnet.net
• Subject: [mg50682] plotting the derivative of a splined/interpolated function
• From: atjurhs at 3drc.com (Todd Jurhs)
• Date: Fri, 17 Sep 2004 01:15:46 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```I'm attempting to read in a time ordered data file, create eiteher a
splined or interpolated data function, take the derivative of the
splined or interpolated function, and plot the resulting velocity
curve.

Here's what I've done:

Reading the Data:
dat2=Import["Documents/Rocketry_Files/MAWD_Flight_Data/bttb_i285r-2.txt","Table"]

Using Interpolating Funtions:
approx=Interpolation[dat2, InterpolationOrder\[Rule]5]
InterpolatingFunction[{{0.,91.}},<>]

checking that it works:
approx[t]/.{t->11.2}
3993.

and plotting the position curve:
Plot[approx[t],{t,0,91}]
I get a nice plot :)

Doing the same thing with the SplineFit function:

<<NumericalMath`SplineFit`

approx2 = SplineFit[dat2, Cubic]
SplineFunction[Cubic, {0., 1820.}, <>]

checking that it works:
approx2[11.2]

{0.56,128.802}

ParametricPlot[approx2[t], {t, 0, 1820},
PlotRange -> All, Compiled -> False]
Again I get a nice plot :)

Taking the derrivative of either the splined or interpolated functions
also seems to work:

dervie[t]=D[approx[t],t]
InterpolatingFunction[{{0.,91.}},<>][t]

dervie[t]/.{t->10.}

220.

AND

dervie2=D[approx2[t],t]
(SplineFunction[Cubic, {0., 1820.}, <>])'[t]

BUT I can't seem to plot either dervie or dervie2 with the standard
Plot ParametricPlot commands

So the question becomes is, how to I plot the derrivative of an
interpolated or slpined function?

Thanks for your help!

```

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