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I would like to differentiate the function s, and be able to evaluate it for different w afterwards. I tried the following:

 s[w_, V1_, V2_, V3_] = -Exp[-(V1 + V2)/2 - V3] + 
  Exp[-(V2 + V1)/2]/(Exp[(V2 - V1)/2] + 
      Exp[-(V2 - V1)/2]) (11 w^2 - (  
       Exp[-V1] +  Exp[-V2]  Exp[-V3] +  Exp[-V2] +  
        Exp[-V1]  Exp[-V3])^2)

D[s[w_, V1, V2, V3], w]

This is what I got

(22 E^(1/2 (-V1 - V2)) w_ 
Pattern^(0,1)[w, _]
)/(E^((V1 - V2)/2) + E^(
 1/2 (-V1 + V2)))

I don't understand why "pattern" shows up in the expression, and what it might mean. I think I might have done something wrong with the patterns, but why don't I just get some kind of error?

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closed as too localized by Szabolcs, halirutan, image_doctor, Artes, rm -rf Dec 19 '12 at 2:29

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1 Answer 1

up vote 2 down vote accepted

This happens because you used a pattern, w_, where it should not be used. Note that the full form of w_ is Pattern[w, Blank[]]. So just change w_ to w in D[s[w_, V1, V2, V3], w].

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Thanks a lot! Originally I had a much more complicated expression, and when leaving out the _ I got something really ugly, while with w_ it did not look so very bad. Is there any meaning to this pattern thing in my final expression, or does it just mean that I did some crap before? –  Apatura Dec 18 '12 at 16:58
@Apatura I'm sorry, but I'm not sure I understand. Why did you put the underscore character there in the first place? If you're not familiar with patterns, you can learn about them here. –  Szabolcs Dec 18 '12 at 17:16
First I did it because I then thought it was right - which it is not, as I know now. But then I wondered why it seemed to make a difference on the output, why it showed up in the middle of the expression and what the (0,1) might mean. –  Apatura Dec 18 '12 at 17:27
@Apatura You'll find the answer if you look at the FullForm of w_. Try writing pattern and blank there to see more clearly what's happening. ^(1,0) means derivative with respect to the first argument. Also, I recommend you look at this tutorial. –  Szabolcs Dec 18 '12 at 20:20

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