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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 ?)




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