Ive come across this derivative question:

The solution is quite simple up until the solution, basically I understand that and that also as shown is the solutions but I fail to understand how the answer: is derived from this point. I have tried integratind what would be the right hand side to the equivalent variable on the LHS and all fails. Im afraid that im only used to perfect derivatives when you can spot the product rule. Any suggestions on th method in such case or how to proceed?