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derivation of a picewise defined function

• To: mathgroup at smc.vnet.net
• Subject: [mg46098] derivation of a picewise defined function
• From: "M.L. Bondar" <mbondar at win.tue.nl>
• Date: Fri, 6 Feb 2004 04:15:21 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

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