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RE: derivation of a picewise defined function
*To*: mathgroup at smc.vnet.net
*Subject*: [mg46118] RE: [mg46098] derivation of a picewise defined function
*From*: "David Park" <djmp at earthlink.net>
*Date*: Sat, 7 Feb 2004 04:02:00 -0500 (EST)
*Sender*: owner-wri-mathgroup at wolfram.com
Luiza,
When one wants to do calculus on piecewise functions it is best to define
them with the UnitStep function.
h[x_] := E^(x - 1) + (x - E^(x - 1))UnitStep[x - 1]
Plot[h[x], {x, 0, 2},
Frame -> True,
PlotRange -> {0, 2}];
j[x_] = h'[x]
E^(-1 + x) + (-E^(-1 + x) + x)*DiracDelta[-1 + x] +
(1 - E^(-1 + x))*UnitStep[-1 + x]
Plot[j[x], {x, 0, 2},
Frame -> True,
PlotRange -> {0, 2}];
David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/
From: M.L. Bondar [mailto:mbondar at win.tue.nl]
To: mathgroup at smc.vnet.net
Hi,
I have the following problem. I need to work with the first derivative
of a picewise defined function.
A simple example :
h[x_] := x /; 1 <= x
h[x_] := E^(x - 1) /; x <= 1
I define
j[x_] := h'[x]
For 1<= x j[x] computes the values, j[x]=1 for all 1<=x, but for
x<=1 it returnes me j[x]=h'[x].
I need also the values of j for x<=1. How can I do that with
Mathematica?
Thank you.
Luiza
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