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I am looking through a journal and I came across a function that I wanted to convert to its differential version using Mathematica.

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Would anyone be able to get the differential version by using mathematica?

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Yes, someone will eventually obtain the differential. For you I suggest first reading this. –  Sektor Nov 3 '13 at 10:17
    
Would you explain why the question is down graded, I understand how it is done by pen and paper, I was purely interested in how to do it in Mathematica! –  ALEXANDER Nov 3 '13 at 13:42
    
Yes, I will. Did you, even for one minute, try to search the Internet for answers ? If you know how to do it using pen'n'paper then you have a fairly good idea about the details. So, you can just search for the appropriate tools and try to solve the problem yourself. I am sorry, I can't see any effort you allegedly put into researching the question. –  Sektor Nov 3 '13 at 14:38
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1 Answer

up vote 2 down vote accepted

The main problem is incorrect syntax. You need to use the following

eq = Log[P[t]/P[t0]] == α (t - t0) + β Log[Q[t]/Q[t0]] + X[t]

Then take derivative with respect to t

D[eq, t]
P'[t]/P[t] == α + β Q'[t]/Q[t] + X'[t]
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why not α `t I see that the expression comes out as with α by itself –  ALEXANDER Nov 3 '13 at 13:48
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@ALEXANDER that's because every other term contains the d/dt operator. You could imagine multiplying both sides with dt and you get the listed result. –  Sjoerd C. de Vries Nov 3 '13 at 13:53
    
Thank you! That makes sense! –  ALEXANDER Nov 3 '13 at 15:18
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