I was reading the lecture notes by Acemoglu and Autor on Labour Economics. https://economics.mit.edu/files/4689
I was able to understand equations 1.1 to 1.8 of the notes; however, I am unable to understand how equations 1.9 and 1.10 were derived from equations 1.8 and 1.9 respectively. I understand that integration and differentiation was applied, but I am not able to figure out the exact steps involved.
For the transition from equation 1.8 to 1.9, I tried to understand in terms of general power rule and general exponential rule of integration, but there are so many terms involved that I am unable to think how these rules apply.
For the transition from 1.9 to 1.10, I tried to understand in terms of general product rule and quotient rule of differentiation, but I am unable to figure out exact steps.
I would deeply appreciate if anyone could help me understand these steps. Please let me know if any other info is required from me.