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MathGroup Archive 1996

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Re: Re: Q: Symbolic manipulation with Mathematica

  • Subject: [mg3037] Re: Re: Q: Symbolic manipulation with Mathematica
  • From: BobHanlon at aol.com
  • Date: 25 Jan 1996 05:29:56 -0600
  • Approved: usenet@wri.com
  • Distribution: local
  • Newsgroups: wri.mathgroup
  • Organization: Wolfram Research, Inc.
  • Sender: mj at wri.com

This is not a general solution.  This works for functions of one or two
variables (x or x and y respectively):

g[func_] := func + x D[func, x];

Format[Derivative[n_, m_:0][func_][var__]] := 
 d^n/dx^n d^m/dy^m func[var];

g[f[x]]

         d f[x]
f[x] + x ------
           dx

g[g[f[x]]] // Simplify

                        2
           d f[x]    2 d  f[x]
f[x] + 3 x ------ + x  -------
             dx            2
                         dx

g[f[x, y]]

            d f[x, y]
f[x, y] + x ---------
               dx

D[g[f[x, y]], y]

               2
d f[x, y]     d  f[x, y]
--------- + x ----------
   dy           dx dy

g[g[f[x, y]]] // Simplify

                              2
              d f[x, y]    2 d  f[x, y]
f[x, y] + 3 x --------- + x  ----------
                 dx               2
                                dx

D[g[g[f[x, y]]], y] // Simplify

                 2               3
d f[x, y]       d  f[x, y]    2 d  f[x, y]
--------- + 3 x ---------- + x  ----------
   dy             dx dy             2
                                  dx  dy

D[f[x, y], {x, m}]

 m
d  f[x, y]
----------
     m
   dx

D[f[x, y], {y, n}]

 n
d  f[x, y]
----------
     n
   dy

D[f[x, y], {x, m}, {y, n}]

 m + n
d      f[x, y]
--------------
     m   n
   dx  dy

However, it does not work for

D[f[y], y]

d f[y]
------
  dx

_______________

Bob Hanlon
bobhanlon at aol.com


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