Use of potentials (electrodynamics, classical)

[bman!!]

hello, I've just gone through a derivation using the vector potential A, and using the equation derived (a wave equation) which arises from using the lorentz gauge, it is applied to the problem of a current sheet in the xy plane, located at z=0 with current in the x direction only. the current varies with time so we are looking for wave solutions propagating in the + and - z directions.

Ive attached the relevant page (its not long at all), and basically my problem is simply: i understand pretty much everything up until equation 6.46, however, i cannot for the life of me understand how he gets to 6.47.

i know its probably something really simple, probably like a nifty application of the chain rule, but Id appreciate if someone could point out the elephant to me becuase i really can't see it and its annoying the hell out of me.

cheers

(im sure the answer will make me feel like an Rtard)

 

[bman!!]

is the picture not working or something? its just a simple boundary (jump?) conditions problem. i say simple, I'm pretty terrible with jump conditions, so any help is really appreciated. this one step is driving me mad!