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Re: derivation of a picewise defined function

• To: mathgroup at smc.vnet.net
• Subject: [mg46139] Re: derivation of a picewise defined function
• From: bobhanlon at aol.com (Bob Hanlon)
• Date: Sat, 7 Feb 2004 04:02:54 -0500 (EST)
• References: <bvvnam$j4h$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Use UnitStep
 
h[x_] := E^(x-1) + UnitStep[x-1]*(x -E^(x-1));
 
j[x_] := Evaluate[Simplify[h'[x]]];
 
j[x]
 
(1 - E^(x - 1))*UnitStep[x - 1] + E^(x - 1)
 
Simplify[j[x], x<1]
 
E^(x - 1)
 
Simplify[j[x], x>1]
 
1
 
 
Bob Hanlon
 
In article <bvvnam$j4h$1 at smc.vnet.net>, "M.L. Bondar" <mbondar at win.tue.nl>
wrote:
 
<< 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?