Derivation Rotemberg pricing

Hello everyone,

I’m struggling in understanding how the authors derived the equation 18 (Rotemberg price adjustment) on page 11.
I tried to take the first derivative of equation 17 with respect to price, but I got stuck.

I would really appreciate your help

Best
kiel-working-paper-1592 (1).pdf (430.0 KB)

Have a look at https://www3.nd.edu/~esims1/new_keynesian_2016.pdf