Re: Total Derivative
- To: mathgroup at smc.vnet.net
- Subject: [mg42092] Re: [mg42088] Total Derivative
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Thu, 19 Jun 2003 03:58:53 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
The total derivative is just the usual partial derivative, except that all variables are assumed to depend on the variable with respect to which the differnetiation is being performed. Now, note that Mathematica assumes that all function are at least of class C2: D[f[x,y],y,x]-D[f[x,y],x,y] 0 The same is true for total derivatives: Dt[f,x,y]-Dt[f,y,x] 0 O.K., now take f=y. Andrzej Kozlowski Yokohama, Japan http://www.mimuw.edu.pl/~akoz/ http://platon.c.u-tokyo.ac.jp/andrzej/ On Wednesday, June 18, 2003, at 03:11 PM, Joel storch wrote: > Dt[x y,x,y] gives 1+dx/dy dy/dx > > I would expect: 1+dx/dy dy/dx + x d/dy (dy/dx) > > Can someone explain this result ? > > >