Re: Implicit Derivatives

• To: mathgroup at smc.vnet.net
• Subject: [mg26206] Re: Implicit Derivatives
• From: "Paul Lutus" <nospam at nosite.com>
• Date: Sat, 2 Dec 2000 02:10:35 -0500 (EST)
• References: <9074vq\$b19@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```"Tom De Vries" <tdevries at shop.westworld.ca> wrote in message
news:9074vq\$b19 at smc.vnet.net...
> 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?

Here is one approach:

f = (3 x y[x] == x^3 + y[x]^3)

soln = Solve[D[f, x], y'[x]]

--

Paul Lutus
www.arachnoid.com

```

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