Learn Turkish: Senin sabırsızlığın yüzünden oyunu kaybettik. - Because of your impatience, we lost the game.

yüzünden (because of / due to) is used for negative causes. To link it to the person or thing causing the issue, Turkish uses a genitive-possessive chain. We use senin (your - genitive) and sabırsızlığın (your impatience - possessive) right before the postposition.

Could I use sayesinde instead of yüzünden here?

Grammatically, yes, because both take the exact same structure. However, sayesinde means "thanks to" and is strictly used for positive outcomes. Since losing a game (oyunu kaybettik) is a negative outcome, yüzünden is the correct choice.

What is the root of sabırsızlığın and why is there a ğ in it?

The root is sabır (patience). Adding -sız makes it sabırsız (impatient), and adding -lık creates the noun sabırsızlık (impatience). When we add the possessive ending -ın to mean "your impatience", the hard k softens to a ğ (sabırsızlığın) because it is trapped between two vowels.

Why is the verb written as kaybettik instead of kayıp ettik?