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MathGroup Archive 2004

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Re: Simply derivative question, Math 5.

  • To: mathgroup at smc.vnet.net
  • Subject: [mg50257] Re: [mg50240] Simply derivative question, Math 5.
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Mon, 23 Aug 2004 06:34:25 -0400 (EDT)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <200408220419.AAA10290@smc.vnet.net>
  • Reply-to: murray at math.umass.edu
  • Sender: owner-wri-mathgroup at wolfram.com

As the Mathematica Book (printed or electronic) explains, ALL built-in 
objects in Mathematica have names that begin with an upper-case letter. 
  So the Napierian "e" is represented by E, not e.  (Or, if you want it 
to   look more like conventional mathematical notation, type Esc e Esc 
to obtain the Mathematica stylized e; in fact, you'll see that stylized 
e in the result.)

So Mathematica was treating e as an unknown constant and gave the 
correct answer.

When e = E, then Log[e] = 1, so no "extra" factor:

   D[(1 + c E^t)/(1 - c E^t), t] // Simplify

By the way, you don't need an explicit multiplication operator after the 
c here -- just a space (so Mathematica can see you have two 
single-letter names rather than a two-letter name cE).

It's REALLY worth a couple hours of your time to read the early material 
in the Mathematica Book!  It will save you a lot of time avoiding such 
basic difficulties.


Ted Kahn wrote:
> Hello- I am trying to take the derivative of the following function:
> 
> (1 + c*e^t)/(1 - c*e^t)
> 
> with respect to t.
> 
> ================
> \!\(Simplify[D[\(1 + c\ e\^t\)\/\(1 - c\ e\^t\), t]]\)
> ============
> 
> The answer I get includes an "extra" Log[e] in the numerator. Am I not  
> using the program correctly or am I not understanding the answer  
> correctly? Other?
> 
> thanks, -ted

-- 
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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