I was overlooking page 47 of "The Physics of the Manhattan Project" 2.2 Critical Mass: Diffusion Theory, and author Bruce Cameron Reed reported that:

Can anyone explain how Bruce Cameron Reed got from (2.18) to (2.19)

I tried plugging ## N(r,t) = N(r) N(t) ## into (2.18) to get (2.19), but it just does not make any sense to me on how there is a fraction of ## \frac{1}{N_r} ## multiplied to the second term after the equals sign

Assuming ## N ## in the first term after the equals sign is ## N(r,t) ## I cannot see how using algebra would allow a person to arrive to (2.19)

I have also tried to take advantage of the relationship

## \Big (\frac{\partial N(r,t)}{\partial t} \Big)_t = N'(t) N(r) ## but even taking advantage of this I still could not figure out how Reed transformed (2.18) to (2.19)