Re: Inplicit differentiation
- To: mathgroup at smc.vnet.net
- Subject: [mg63559] Re: Inplicit differentiation
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Thu, 5 Jan 2006 03:12:27 -0500 (EST)
- Organization: The Open University, Milton Keynes, UK
- References: <dpg0k4$piu$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Fernando Rodríguez wrote:
> Hi,
>
> How can I ask Mathematica to differentiate a function if y is not easily
> isolated? For instance:
>
> x^2 y + (y + x)^3 = 0
>
> If I call D[x^2 y + (y + x)^3 == 0, x] it won't return the correct answer,
> as it will consider y a constant.
>
> Thanks!
>
>
Hi Fernando,
You must indicate to Mathematica that the symbol y is a function that
depends on x or at least that y is not a constant. If you want an
explicit formula for y' you can try *Solve* as in input [3].
In[1]:=
D[x^2*y[x] + (y[x] + x)^3 == 0, x]
Out[1]=
2*x*y[x] + x^2*Derivative[1][y][x] + 3*(x + y[x])^2*(1 +
Derivative[1][y][x]) == 0
2 2
(that is 2 x y[x] + x y'[x] + 3 (x + y[x]) (1 + y'[x]) == 0)
In[2]:=
D[x^2*y + (y + x)^3 == 0, x, NonConstants -> y]
Out[2]=
2*x*y + x^2*D[y, x, NonConstants -> {y}] + 3*(x + y)^2*(1 + D[y, x,
NonConstants -> {y}]) == 0
In[3]:=
Solve[D[x^2*y[x] + (y[x] + x)^3 == 0, x], Derivative[1][y][x]]
Out[3]=
2 2
-3 x - 8 x y[x] - 3 y[x]
{{y'[x] -> --------------------------}}
2 2
4 x + 6 x y[x] + 3 y[x]
Hope this helps,
/J.M.