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