       Re: Re: Correction to "Fundamental Theorem of Calculus

• To: mathgroup at smc.vnet.net
• Subject: [mg100763] Re: [mg100747] Re: Correction to "Fundamental Theorem of Calculus
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Sat, 13 Jun 2009 06:03:26 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <h0sbtl\$hdk\$1@smc.vnet.net> <200906120946.FAA27926@smc.vnet.net>

```Yes. However, with those definitions of f and g:

f'[x]
Sin[x^2]

g'[x]
0

I believe that's the discrepancy to which the original poster refers.
And this originates from what you'll see if you use the FullForm, the
FullForm of h'[x] being Derivative[h][x]:

Derivative[f]
(FresnelS^\[Prime])[Sqrt[2/\[Pi]] #1]&

Derivative[g]
0&

The latter arises from:

g[x]
1/2 Sqrt[\[Pi]] Erf[x]

So I don't understand why the derivative of g is the constantly 0
function. After all, Mathematica DOES know:

Derivative[Erf]
(2 E^-#1^2)/Sqrt[\[Pi]]&

And that surely is not the zero function!

Simon wrote:
> Hi Len,
>
> Running both 6.0.3 and 7.0.1, I don't seem to get that problem:
>
> In:= f[x_]:=Integrate[Sin[t^2],{t,0,x}]
>
> In:= D[f[x],x]
> Out= Sin[x^2]
>
> In:= g[x_]:=Integrate[Exp[-t^2],{t,0,x}]
>
> In:= D[g[x],x]
> Out= E^-x^2
>
> Simon
>

--
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

```

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