Re: Problems with differentiating Piecewise functions

• To: mathgroup at smc.vnet.net
• Subject: [mg86970] Re: Problems with differentiating Piecewise functions
• From: "David Park" <djmpark at comcast.net>
• Date: Thu, 27 Mar 2008 08:20:39 -0500 (EST)
• References: <fsd6ph\$9hb\$1@smc.vnet.net>

```Although you can often get away with argumentless definitions, I think it is
always better to define functions with argument patterns.

pw1[x_] = Piecewise[{{x^2, x <= 0}, {x, x > 0}}]

Then you can get the derivative by simply writing

pw1'[x]

The derivative is undefined at x == 0 so Mathematica is correct.

--
David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/

"hlovatt" <howard.lovatt at gmail.com> wrote in message
news:fsd6ph\$9hb\$1 at smc.vnet.net...
> 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.
>

```

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