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MathGroup Archive 2000

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Re: Implicit Derivatives

  • To: mathgroup at smc.vnet.net
  • Subject: [mg26208] Re: Implicit Derivatives
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Sat, 2 Dec 2000 02:10:36 -0500 (EST)
  • Organization: Universitaet Leipzig
  • References: <9074vq$b19@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,
not much better but you can use total derivatives
eq = (3 x y == x^3 + y^3)

deqn = (Dt /@ eq) /. a_ == b_ :> a - b == 0 // Simplify

Solve[deqn /. c_ == a_.Dt[x] :> c/Dt[x] == a /. Dt[y]/Dt[x] -> y', y']

Regards
  Jens

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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