Re: Implicit Derivatives

• To: mathgroup at smc.vnet.net
• Subject: [mg26215] Re: [mg26193] Implicit Derivatives
• From: BobHanlon at aol.com
• Date: Sat, 2 Dec 2000 02:10:41 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

eq = (3 x y == x^3 + y^3);

Solve[D[eq /. y -> y[x], x], y'[x]] // Simplify

{{Derivative[1][y][x] -> (x^2 - y[x])/(x - y[x]^2)}}

Solve[Dt[eq, x], Dt[y, x]] // Simplify

{{Dt[y, x] -> (x^2 - y)/(x - y^2)}}

Solve[Dt[eq], Dt[y]] // Simplify

{{Dt[y] -> ((x^2 - y)*Dt[x])/(x - y^2)}}

Bob Hanlon

In a message dated 11/30/00 10:30:32 PM, tdevries at shop.westworld.ca writes:

>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?
>

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