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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?
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