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