RE: derivation of a picewise defined function

*To*: mathgroup at smc.vnet.net*Subject*: [mg46118] RE: [mg46098] derivation of a picewise defined function*From*: "David Park" <djmp at earthlink.net>*Date*: Sat, 7 Feb 2004 04:02:00 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Luiza, When one wants to do calculus on piecewise functions it is best to define them with the UnitStep function. h[x_] := E^(x - 1) + (x - E^(x - 1))UnitStep[x - 1] Plot[h[x], {x, 0, 2}, Frame -> True, PlotRange -> {0, 2}]; j[x_] = h'[x] E^(-1 + x) + (-E^(-1 + x) + x)*DiracDelta[-1 + x] + (1 - E^(-1 + x))*UnitStep[-1 + x] Plot[j[x], {x, 0, 2}, Frame -> True, PlotRange -> {0, 2}]; David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ From: M.L. Bondar [mailto:mbondar at win.tue.nl] To: mathgroup at smc.vnet.net 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