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Re: Incoherent value for partial derivative

• To: mathgroup at smc.vnet.net
• Subject: [mg91068] Re: Incoherent value for partial derivative
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Tue, 5 Aug 2008 04:02:26 -0400 (EDT)

On 8/4/08 at 3:26 AM, misvrne at gmail.com (Miguel) wrote:

>Let

>In[1]: g[x_]:=3x^2+5x; FullForm[g'[x]]

>Out[1]: Plus[5,Times[6,x]]

>In[2]: g'[2] Out[2]: 17

>Mathematica works fine and the result is correct. First, it executes
>the derivation and then the delayed substitution/assignation.

Unless I had either tested this or found something specific in
the documentation to say things would work this way, I would not
have relied on this particular sequence of execution. Without
checking, I would have expected Mathematica to substitute a
particular value for x then take the derivative getting 0 since
f evaluates as a constant.

>But for partial derivative Mathematica works different way (not
>correspondig to FullForm

This really isn't a correct conclusion. FullForm[expr] gives the
form corresponding to the evaluation of expr.

>In[3]: f[x_,y_]:=x^2+x y^2; FullForm[\!\(
>\*SubscriptBox[\(\[PartialD]\), \(x\)]\ \(f[x, y]\)\)]

>Out[3]: Plus[Times[2,x],Power[y,2]]

>In[4]: \!\( \*SubscriptBox[\(\[PartialD]\), \(x\)]\ \(f[1, 2]\)\)
>Out[4]: 0

Here, the sequence of evaluation is more along the lines of what
I would expect. That is values for x and y are substituted
resulting in a real value then the derivative is computed. You
can verify this works as I've described by using Trace.