Kate Hudson Shows off Baby Girl Rani in New Photo: 'Early Morning Calm'

Kate Hudson is enjoying the little moments with daughter Rani Rose Hudson Fujikawa.

On Thursday, the 39-year-old actress shared her second photo of newborn daughter Rani, her little bundle of joy and newest addition to the family sleeping peacefully in her arms.

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(Photo: Instagram / @katehudson)

"The early morning calm," Hudson captioned the image, using the hashtag "#babybubble."

Hudson and boyfriend Danny Fujikawa welcomed their baby girl, their first child together, on Tuesday, Oct. 2, with the 39-year-old actress making the announcement on her Instagram account. She also explained the meaning behind her baby girl's name, which is pronounced like "Ronnie."

"We have decided to name our daughter Rani (pronounced Ronnie) after her grandfather, Ron Fujikawa. Ron was the most special man who we all miss dearly. To name her after him is an honor," Hudson explained on Instagram. Fujikawa's father, Ron, died in October 2012.

"Everyone is doing well and happy as can be," she wrote at the time. "Our family thanks you for all the love and blessings that have been sent our way and we send our right back."

Over the course of her pregnancy, the social media platform became a place where the actress could document her growing baby bump, sharing the journey with her fans, a trend that she continued after Rani made her arrival into the world. Just four days after giving birth, Hudson shared the first photo of her little girl.

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(Photo: Instagram / @katehudson)

"Our little rosebud," Hudson captioned the image of Rani swaddled in a striped blanket and wearing a pink hat with a bow.

Hudson and Fujikawa, who announced that they were expecting in April, had reportedly had babies on the mind for some time, with a source stating following the pregnancy reveal that Hudson had been hoping for a little girl. Now, the new family is seamlessly adjusting to life with a newborn.

"She's always wanted a daughter so this is really a dream come true," a source told PEOPLE. "And her big brothers are so excited — they'll be so protective and sweet to her always."

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While Rani is Fujikawa's first child, she joins Hudson's two sons – 7-year-old son Bingham Hawn from her relationship with ex-fiancé Matt Bellamy, and 14-year-old son Ryder Russell from her marriage to ex-husband Chris Robinson. The actress previously revealed during an appearance on SiriusXM in 2016 that she was hoping to see her family expand, stating her desire to have "anywhere between four and six" children.