Derrochaste comes from the verb derrochar, which typically means to squander, waste, or lavishly spend money.
In this bachata song, Romeo Santos sings "Derrochaste sentimientos" (You squandered feelings) to describe how his partner poured out her precious emotions on past lovers who didn't understand her. This vivid financial metaphor makes it a truly memorable way to express the feeling of giving your heart to the wrong people.
Romeo Santos is known as the King of Bachata, and this song is a perfect example of why. He gets straight to the point, telling his lover he doesn't care at all about her past. He's incredibly direct about it, saying things like, "No juzgo a tu pasado ni mala reputación" (I don't judge your past or your bad reputation). He even makes a joke that the only person who was a saint was Mother Teresa, so who is he to judge? He's fully aware of her history, even saying the pillow has told him it's "presenciado mucho sexo en tu colchón" (witnessed a lot of sex on your mattress).
But the whole point of the song is that none of that matters. He believes he's different from everyone who came before. While others may have been with her physically, he claims "Solo yo llegué al alma" (Only I reached your soul). He admits he's no saint himself, with a clever line playing on his own name: "De santo solo tengo el apellido" (Of saint, I only have the last name). For him, all her past experiences were just a search, and he is the final destination. The physical connection is there, but the real prize is the emotional one he believes only he has, insisting that she's only ever made true love with him: "Pero el amor solo conmigo" (But love, only with me).