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>
- Reply-to: murray at math.umass.edu
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[1][h][x]:
Derivative[1][f]
(FresnelS^\[Prime])[Sqrt[2/\[Pi]] #1]&
Derivative[1][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[1][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[1]:= f[x_]:=Integrate[Sin[t^2],{t,0,x}]
>
> In[2]:= D[f[x],x]
> Out[2]= Sin[x^2]
>
> In[3]:= g[x_]:=Integrate[Exp[-t^2],{t,0,x}]
>
> In[4]:= D[g[x],x]
> Out[4]= 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
- References:
- Re: Correction to "Fundamental Theorem of Calculus and Mathematica"
- From: Simon <simonjtyler@gmail.com>
- Re: Correction to "Fundamental Theorem of Calculus and Mathematica"