Derivative of Axial Resolution from Rayleigh's Limit

[TS Wong]

I am currently studying optical microscope and discover that the axial resolution is limited as r(z) = 2pi / (NA)^2.
However, while I got hints that it is due to the Rayleigh's limit, I can't derivative the equation using numerical method.
It would be huge thanks if anyone can help me on the solution.

 

[Andy Resnick]

Born and Wolf derive this in section 8.8 (7th edition). My hint is that you are evaluating the diffraction integral on-axis.