Re: Re: Q: Symbolic manipulation with Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg3037] Re: Re: Q: Symbolic manipulation with Mathematica
- From: BobHanlon at aol.com
- Date: Thu, 25 Jan 1996 03:20:26 -0500
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 ==== [MESSAGE SEPARATOR] ====