How do you apply the Chain Rule to the energy distribution function?

[gareth]

Hi guys,

I have a problem understanding the derivation of the energy distribution function; i.e. the number of particles dN with energy dE,

here is what I have (from literature);

dN/dE = dN/dt * dt/dV * dV/dE

so you can define some of these whole derivitives in terms of acceleration (dV/dT), the number of particles you count per unit time (dN/dT) and how velocity varies with energy dV/dE,

So after plugging in the known quantitites, you end up with something like

dN/dE = dN/dt * -t^3 / md^2

where,

t = time
N = number of particles
m = mass
d = distance

Now here's my problem, I know that breaking up the dN/dE term into separate differentiable components make it easier to solve in terms of know quantities ( m,t,d etc.) but what I don't understand is how you get from dN/dE to dN/dt * dt/dV * dV/dE, so in other words, what's the formal procedure for seperating out the derivitaves.

Hopefuly this is straightforward enough (for you),

Thanks
G

 

[marcusl]

It's called the Chain Rule of calculus. Just google chain rule and you'll see a hundred explanations and tutorials.

Here are two:

http://mathworld.wolfram.com/ChainRule.html"

http://www.math.hmc.edu/calculus/tutorials/chainrule/"

Better is to look in any college calculus text (like those by Thomas).