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Problems with differentiating Piecewise functions

• To: mathgroup at smc.vnet.net
• Subject: [mg86930] Problems with differentiating Piecewise functions
• From: hlovatt <howard.lovatt at gmail.com>
• Date: Wed, 26 Mar 2008 04:55:41 -0500 (EST)

If I set up a piecewise function and differentiate it:

In[112]:= pw1 = Piecewise[{{x^2, x <= 0}, {x, x > 0}}]

Out[112]= \[Piecewise] {
  {x^2, x <= 0},
  {x, x > 0}
 }

In[113]:= pw1 /. x -> 0

Out[113]= 0

In[114]:= pw1d = D[pw1, x]

Out[114]= \[Piecewise] {
  {2 x, x < 0},
  {1, x > 0},
  {Indeterminate, \!\(\*
     TagBox["True",
      "PiecewiseDefault",
      AutoDelete->False,
      DeletionWarning->True]\)}
 }

In[115]:= pw1d /. x -> 0

Out[115]= Indeterminate

Then at the joins between the pieces I get Indeterminate values,
because the limit x <= 0 has become x < 0 after differentiation. Does
anyone know a solution to this problem?

Thanks,

Howard.

• Follow-Ups:
  • Re: Problems with differentiating Piecewise functions
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>