       Differentiation and Polynomial questions

• To: mathgroup at smc.vnet.net
• Subject: [mg20704] Differentiation and Polynomial questions
• From: "Danny Mathews" <dmathews at ticnet.com>
• Date: Mon, 8 Nov 1999 02:48:47 -0500
• Sender: owner-wri-mathgroup at wolfram.com

```I was using the "StepbyStepDifferentiation" package I found on the web site
and it has raised a question for me.

It seems that Mathematica ignores the Quotient Rule in general and uses the
Product Rule for equations in a f(x)/g(x) format.

This leaves the solution in a f(x) + g(x) format that I have to simplify to
get the answer to agree with what I came up with using a pencil or on my
TI-89 calculator.

An example is (1+x^2)/(1-x^2).  I came up with(as did my TI-89)
4x/((x^2-1)^2) for a solution.

Mathematica gives a answer in the form of f(x) + g(x) that will simplify to
the solution above.  I tried several examples with the same scenario.  Is

Also, Mathematica displays polynomials with the powers written in ascending
order which is opposite of how I was taught to write polynomials in standard
form.  Can this be changed?

Bonus Question:

My Calculus instructor loves piece-wise functions.  Any info on plotting