       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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