       Re: how can one use mathematica get the approximate derivative of {x,y} data points?

• To: mathgroup at smc.vnet.net
• Subject: [mg124272] Re: how can one use mathematica get the approximate derivative of {x,y} data points?
• From: Michael Stern <nycstern at gmail.com>
• Date: Sun, 15 Jan 2012 04:50:05 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201201140753.CAA01265@smc.vnet.net>

```Mathematica will cheerfully take derivatives of InterpolationFunctions.

In:= data = {{0.03512, -0.5}, {0.0351181, -0.499}, {-.05, 1}, {0, 9}, {-0.113972,
0.699}, {-0.115072, 0.7}};
In:= ifun = Interpolation[data]

You may want to play with the InterpolationOrder in step 2, but something along these lines should work.
You can sanity check the results with a graph of this sort:

In:= Plot[{ifun'[x], ifun[x]}, {x, -.115, .15}, PlotRange -> All]

And if you want the answer as a table of points rather than a continuous function, you can produce such a table with

In:= Table[{x, ifun'[x]}, {x, -.115, .15, .005}]

or the equivalent.

Cheers,

Michael Stern

On Jan 14, 2012, at 2:53 AM, Michael B. Heaney wrote:

> Hi,
>
> I have a set of {x,y} data points:
>
> {{0.03512, -0.5}, {0.0351181, -0.499}, ... {-0.113972, 0.699}, {-0.115072,
> 0.7}}
>
> These data points look like a function y=f(x) when plotted on the x-y axes.
> However, I do not know what the function f(x) is. But I need to get the
> approximate derivative df/dx, as another set of data points. How can one
> use Mathematica to do this?
>
> Thanks,
>
> Michael
>
> --

```

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