Kanye West Dotes on Newborn Daughter, Hasn't Left Kim Kardashian's Side

06/20/2013 at 12:05 PM EDT

Kanye West Making Sure 'Everything Is Perfect' For Kim Kardashian & Baby
Kim Kardashian and Kanye West
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Kanye West

Kanye West

Kanye West is taking his daddy duties very seriously.

The Yeezus rapper – who rushed to Kim Kardashian's side when she went into labor – has been doting on his baby daughter.

"Kanye hasn't left Kim and the baby's side," a source close to Kardashian, 32, tells PEOPLE. "He's been in the room for days making sure everything is perfect for the two of them."

With her boyfriend there, the usually open Kardashian – who was admitted to the hospital with medical complications on June 14 – is savoring her privacy.

According to a source, "Kim is being very protective of the baby."

• With Reporting By JENNIFER GARCIA

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