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>