well, the another one...
give up... is a phrasal verb, which means to stop trying, or doing something. (surrender, abandon habit, addiction, etc.) the order of the particle it doesn't matter.
I want to give up smoking
Many women give themselves up to raising their family. ( Muchas mujeres se dedican enteramente a criar a su familia.)
My father didn't give me up.- Mi padre no se daría por vencido (easily with me, because is my father, he loves me, and he's trying and trying with me)
Well. I hope I've been able to help you. as I told you. I'm a student too. Maybe a native wants to give us a wide explanation, to clear your doubts if I've made mistakes.