Re: Problems with differentiating Piecewise functions

• To: mathgroup at smc.vnet.net
• Subject: [mg86938] Re: Problems with differentiating Piecewise functions
• From: Szabolcs Horvát <szhorvat at gmail.com>
• Date: Thu, 27 Mar 2008 08:14:39 -0500 (EST)
• Organization: University of Bergen
• References: <fsd6ph\$9hb\$1@smc.vnet.net>

```hlovatt wrote:
> 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?

Mathematically it makes sense.  The derivative cannot be defined in that
point.  You could manually replace Indeterminate with whichever value
you need there:

D[pw1, x] /. Indeterminate -> a

or

D[pw1, x] /. Indeterminate -> 0

```

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