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MathGroup Archive 2000

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Re: Implicit Derivatives

  • To: mathgroup at smc.vnet.net
  • Subject: [mg26205] Re: [mg26193] Implicit Derivatives
  • From: Jacqueline Zizi <jazi at club-internet.fr>
  • Date: Sat, 2 Dec 2000 02:10:35 -0500 (EST)
  • References: <200012010302.WAA11206@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Just write things as simply as they are:

Solve[D[3 x y[x] == x^3 + y[x]^3, x], y'[x]]

will work.

you occult that y is a function of x. You might be used to it but probably your
students are not. A very  important point of Mathematica  is that reflexion on
what you are doing helps you programming and teaching and searching. From my
point of view it is far from everything else the greatest point that Stephen
Wolfram and his team brings us.

When you understand that 3 x y == x^3 + y^3 makes no sens as it is, you
understand why the solution you point out is cheating to fall back on its feet.

Anyway, having 4 new symbols for 4 lines is, from my point of view, a very
awkward way of programming. You don't need any new symbol to solve this
equation. Just like in Mathematics, "a good definition is a definition that you
use a lot" (Jean Bénabou, our French leader in category theory)


Jacqueline Zizi
------------------

Tom De Vries wrote:

> Hello everyone,
>
> I am teaching a high school calculus class and we are using Mathematica for
> part of the course work.   In the book CalcLabs with Mathematica  they give
> a procedure for finding an Implicit Derivative.    Here is an example with a
> familiar equation....
>
> eq = (3 x y == x^3 + y^3)
>
> eqNew = eq /. y -> y[x]
>
> deqNew = D[eqNew, x]
>
> soln = Solve[deqNew, y'[x]]
>
> I am wondering if there are other ways to get a similar result to this.
> This method makes sense to me but I wondered if there was a more direct
> approach?   I could not find any information using the Help feature but
> perhaps I was just looking in the wrong places?
>
> Thanks,
>
> Tom De Vries
> Alberta, Canada



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