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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