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Re: Simple Differentiation?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg46036] Re: Simple Differentiation?
*From*: Bill Rowe <readnewsciv at earthlink.net>
*Date*: Tue, 3 Feb 2004 03:21:16 -0500 (EST)
*Sender*: owner-wri-mathgroup at wolfram.com
On 2/2/04 at 5:21 AM, pinnama at cims.nyu.edu (Sunil Pinnamaneni)
wrote:
>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 think your problem is a misunderstanding of Mathematica syntax.
dx(f[x]+g[x]) is not the derivative. Instead it is interpreted by Mathematica as the product of a variable dx and the sum of two functions, g and f. So if you literally typed dx(f[x]) you should have gotten the result dx f[x] not f'[x] as you've indicated.
Now assuming you did ask Mathematica to take the derivative of f[x] then Mathematica would correctly return f'[x] since you have not defined either f[x] or f'[x]. What you have defined is the sum of the derivatives for g and f.
Specifically, doing
D[f[x]+g[x], x]
results in 0 according to your definition above
But D[f[x],x] + D[g[x], x] results in f'[x] + g'[x]
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