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Re: Turning Derivative into Function (Newbie Question)

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  • Subject: [mg115462] Re: Turning Derivative into Function (Newbie Question)
  • From: Just A Stranger <forpeopleidontknow at gmail.com>
  • Date: Tue, 11 Jan 2011 19:22:07 -0500 (EST)

Thanks guys! That pure function approach looks the most concise...that would
be the best approach with regards to Mathematica's design philosophy?

I'll sink my teeth into the documentation. :)

On Tue, Jan 11, 2011 at 7:10 AM, Murray Eisenberg <murray at math.umass.edu>wrote:

> Because g is NOT a "function" when you set:
>
>  g := f'[x]
>
> (No more than f would be had you started with f := x^2.)
>
> Whenever you now call g, you get the value of f[x], namely, 2x.
>
> If you really want to define g that way, then you can use a rule and
> replacement:
>
>  g /. x-> 2
>
> But it's probably better to do things like this:
>
>  Clear[g]
>  g[x_] = f'[x]   (* note Set, =, not SetDelayed, := *)
>  g[2]
> 4
>
> Or, if you prefer a more functional approach:
>
>  Clear[g]
>  g = f'
>  g[2]
> 4
>
>
> On 1/11/2011 6:58 AM, Just A Stranger wrote:
>
>> When I apply a function that outputs another function, how come I can not
>> pass arguments to the new function? Am I missing some principle about how
>> Mathematica functions work? Could someone please point me to the relevant
>> documentation?
>>
>>
>> A simple example to illustrate my confusion:
>>
>> In[1]: f[x_] := x^2
>> In[2]: g := f'[x]
>>
>> So now I have:
>>
>> In[3]: g
>> out[3]: 2x
>>
>> as expected
>>
>> So how come I get the following when trying to pass an argument to g:
>>
>> In[4]: g[2]
>> Out[4]: 2x[2]
>>
>> Instead of the output I want:
>>
>> *Ou[4]: 4
>>
>>
>> I tried
>>
>> In: g[x_] := f'[x]
>>
>> But it seems to think I'm trying to assign a function to Times.
>> "SetDelayed::write: Tag Times in (2 x)[y_] is Protected.>>"
>>
>> Thank you very much for any help :)
>>
>>
>>
> --
> Murray Eisenberg                     murray at math.umass.edu
> Mathematics & Statistics Dept.
> Lederle Graduate Research Tower      phone 413 549-1020 (H)
> University of Massachusetts                413 545-2859 (W)
> 710 North Pleasant Street            fax   413 545-1801
> Amherst, MA 01003-9305
>


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