Re: Implicit differentiation
- To: mathgroup@smc.vnet.net
- Subject: [mg11457] Re: Implicit differentiation
- From: Paul Abbott <paul@physics.uwa.edu.au>
- Date: Thu, 12 Mar 1998 01:34:10 -0500
- Organization: University of Western Australia
- References: <6dqqlo$rkc@smc.vnet.net>
MAvalosJr wrote:
> Any ideas how I can plug into mathematica to find the 2nd or third
> derivative of an implicit function? The first derivative is okay. I'm
> using( Example): in:eq= x^3 + y^3 ==2
> in: step1= Dt[eq,x]
> in: step2=Solve[step1, Dt[y,x] (* This
> gives me the first derivative*).
In[1]:= eqn = x^3 + y^3 == 2;
Solve for Dt[y,x]:
In[2]:= Dt[y,x]^=Dt[y,x]/. Solve[Dt[eqn,x], Dt[y,x]]//First
2
x
Out[2]= -(--)
2
y
Using ^= attaches the value of Dt[y,x] to x (not to Dt which is
protected).
Now we can use NestList to compute higher derivatives:
In[3]:= NestList[Dt[#, x] & , Dt[y, x], 2]
2 4 6 3
x -2 x 2 x -10 x 12 x 2 Out[3]= {-(--), ----- -
---, ------ - ----- - --}
2 5 2 8 5 2
y y y y y y
Cheers,
Paul
____________________________________________________________________
Paul Abbott Phone: +61-8-9380-2734
Department of Physics Fax: +61-8-9380-1014
The University of Western Australia Nedlands WA 6907
mailto:paul@physics.uwa.edu.au AUSTRALIA
http://www.pd.uwa.edu.au/~paul
God IS a weakly left-handed dice player
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