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RE: derivation of a picewise defined function

• To: mathgroup at smc.vnet.net
• Subject: [mg46112] RE: [mg46098] derivation of a picewise defined function
• From: "Florian Jaccard" <florian.jaccard at eiaj.ch>
• Date: Sat, 7 Feb 2004 04:01:55 -0500 (EST)
• Reply-to: <florian.jaccard at eiaj.ch>
• Sender: owner-wri-mathgroup at wolfram.com

Use UnitStep :

h[x_] := UnitStep[x - 1]*x + UnitStep[-(x - 1)]E^(x - 1)

h[x] can be derivated, integrated, ploted, etc.
It's a good way to define picewise functions.

Meilleures salutations

Florian Jaccard


-----Message d'origine-----
De : M.L. Bondar [mailto:mbondar at win.tue.nl]
Envoyé : ven., 6. février 2004 10:15
À : mathgroup at smc.vnet.net
Objet : [mg46098] derivation of a picewise defined function


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