Re: Implicit differentiation
- To: mathgroup@smc.vnet.net
- Subject: [mg11406] Re: Implicit differentiation
- From: Allan Hayes <hay@haystack.demon.co.uk>
- Date: Sun, 8 Mar 1998 20:13:26 -0500
- References: <6dqqlo$rkc@smc.vnet.net>
MAvalosJr wrote:
>
> Dear Sirs:
>
> 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]:=
eq[n_]=Dt[x^3 + y^3 ==2,{x,n}];
In[2]:=
Solve[{eq[1],eq[2]}, Dt[y,{x,2}],{Dt[y,{x,1}]}]
(* the {Dt[y,{x,1}]} asks for Dt[y,{x,1}] not to appear in the
solution*)
Out[2]=
4 3
-2 (x + x y )
{{Dt[y, {x, 2}] -> --------------}}
5
y
If you are want more derivatives you might program the process, for
example:
In[3]:=
dt[n_ ]:=
Solve[Table[eq[i],{i,n}],
Dt[y,{x,n}], Table[Dt[y,{x,i}],{i,n-1}]]
In[4]:=
dt[3]
Out[4]=
6 3 3 6
-2 (5 x + 6 x y + y ) {{Dt[y, {x, 3}] ->
------------------------}}
8
y
--
Allan Hayes
Training and Consulting
Leicester, UK
hay@haystack.demon.co.uk
http://www.haystack.demon.co.uk
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