Simple Differentiation?

*To*: mathgroup at smc.vnet.net*Subject*: [mg46014] Simple Differentiation?*From*: "Sunil Pinnamaneni" <pinnama at cims.nyu.edu>*Date*: Mon, 2 Feb 2004 05:21:28 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

In Mathematica 5.0, if one types in: f[x_]+g[x_]^:=1 (1) and then types dx(f[x]+g[x]) we get 0. However, if we type dx(f[x]) + dx(g[x]) after typing (1), we get f'[x] + g'[x]. Mathematica doesn't recognize that f'[x]+g'[x]= dx(f[x]+g[x]), which equals 0. How does one get Mathematica to do this? I'm interested in more complicated examples, which involve more complex differential relations, but I should be able to do things in those situations given a nice, natural way of handling this toy case. Though this seems like a pretty simple thing, I wasn't able to find any thing in the Mathematica Book or elsewhere, which would help with this type of things. Thanks, Sunil