Symbolic Derivative of Piecewise Contin Fcn
- To: mathgroup at smc.vnet.net
- Subject: [mg15490] Symbolic Derivative of Piecewise Contin Fcn
- From: sullivan at indra.com (Steve Sullivan)
- Date: Mon, 18 Jan 1999 04:22:33 -0500
- Sender: owner-wri-mathgroup at wolfram.com
How can I get a symbolic derivative on a region of a piecewise continuous function using Mathematica? Two simple examples, extracted from long Modules are below. Alternatively, is there some magic functional M that, given a piecewise contin function, would return a piece of it? For example, let: f[x_] := If[ x < 0, x^2, x^5] Is there a M such that: M[ f, {x < 0}] would return: x^2 Many thanks for any help ... Steve The following examples of the failure of D[] are extracted from much more complicated functions. They were run using Mathematica 3.0. htest[ uval_ ] := Module [ {res}, If[ uval < 0, res = uval^2, res = uval^5]; res ] D[ htest[ uval], uval] ==> returns: 0 tstb[ pow_Integer, uval_ ] := Module [ {res}, (* local vars *) If[ pow == 0, If[ uval < 0, res = 0, res = uval^2], res = uval^5 * tstb[ pow-1, uval] ]; res (* return *) ] D[ tstb[ 0, uval], uval] ==> returns: 0 D[ tstb[ 1, uval], uval] ==> returns: 5 res$4 uval^4 (?? what is res$4 ?)