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MathGroup Archive 2001

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Re: Deriviation d/dt(x(t))

  • To: mathgroup at smc.vnet.net
  • Subject: [mg27442] Re: [mg27407] Deriviation d/dt(x(t))
  • From: BobHanlon at aol.com
  • Date: Sun, 25 Feb 2001 20:55:46 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Dt[x^2 + y^2 == r^2, t, Constants -> {r}]

2*x*Dt[x, t, Constants -> {r}] + 
   2*y*Dt[y, t, Constants -> {r}] == 0

or

Dt[x^2 + y^2 == r^2, t] /. Dt[r, t] -> 0

2*x*Dt[x, t] + 2*y*Dt[y, t] == 0

or

D[x[t]^2 + y[t]^2 == r^2, t]

2*x[t]*Derivative[1][x][t] + 2*y[t]*Derivative[1][y][t] == 0


Bob Hanlon

In a message dated 2001/2/25 1:14:25 AM, maier1 at sbox.tu-graz.ac.at writes:

>I have a problem, having a definition of a circle: x^2+y^2=r^2
>Where x and y are functions of the time:  x(t), y(t) and r ist a constant.
>
>Now I want to deriviate the equation to get the velocity vector.
>It should be : 2 x dx/dt +2 y dy/dt = 0
>
>Can anyone tell me how to do?
>


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