# I don't get this expansion

1. Apr 1, 2013

### M. next

The equation says: d(lnW)=Ʃ$_{i}$(dlnW$_{i}$/dN$_{i}$)*dN$_{i}$

I chose the constants as so since I ran across this in a Physical problem, but it doesn't matter. It is the maths that I don't understand.

2. Apr 1, 2013

### HallsofIvy

It would help if you explained what W and Wi meant and how they are related.

3. Apr 1, 2013

### M. next

I guess it is only a mathematical relation. Some rule that am not getting.. But if that would help, summation of Wi's will give W. These are related to thermodynamics particularly statistical physics, "W" can be for Maxwell Boltzmann, Bose-Einstein, and so on.. But I am pretty sure that these that I just defined have nothing to do with the expansion above.
Thanks!

4. Apr 1, 2013

### M. next

Please note that IN THE FRACTION above in my first post (in the question) the derivatives are not total derivatives but instead are partial derivatives, ONLY the derivatives included in the fraction - the last derivative is excluded from this correction, i.e it is a total derivative. Sorry about that.

5. Apr 2, 2013

### DeIdeal

Well, that makes more sense. It's just the definition of a total differential. For a function f of n variables

$$\mathrm{d}f(x_{1},x_{2},\ldots,x_{n})=\sum_{i=1}^{n}\frac{\partial{f}}{\partial{x_{i}}}\mathrm{d}x_{i}$$

They are often encountered in thermodynamics. Do you have problems actually calculating them, or was it just the notation that was the problem?

6. Apr 6, 2013