derivative of cubic spline

• To: mathgroup at smc.vnet.net
• Subject: [mg66543] derivative of cubic spline
• From: "Jaccard Florian" <Florian.Jaccard at he-arc.ch>
• Date: Fri, 19 May 2006 03:40:20 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Dear All,

I would like to know how to derivate a spline function constructed by
Mathematica.

The question has already been posted in :
[mg25221] First derivative of interpolated spline

But I wasn't able to find an answer in mathgroup.

Example :

data={{0, 1}, {1, 2.3}, {2, 2.5}, {3, 1.2}, {4, 0.47},
{5, 0.38}, {6, 0.76}}

<< "Numericalmath`SplineFit`"

s = SplineFit[data, Cubic];

You can see that the spline is good :

ParametricPlot[s[x], {x, 0, 6}, PlotStyle -> Blue,
Epilog -> {{Blue, Text[HoldForm[y = s(x)],
{2.5, g1[2.5]}, Background -> White]},
({PointSize[0.03], Red, Point[#1]} & ) /@ data},
PlotRange -> {-0.5, 3}, TextStyle ->
{FontFamily -> Times}];

But D[s[t],t] or s'[t] or so one doesn't help...
So I'm not able to see that the spline is better than Interpolation (in
the sense of a continuous derivative)!

It's the first time I found something that is easier in MathCad than in
Mathematica...

Regards

F.Jaccard
florian.jaccard at he-arc.ch

```

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