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?