Daddy's girl! Mark Zuckerberg takes break from two month's paternity leave to post touching photo with baby Maxima and reveals 'everyone is doing great'  

She's heir to his $46 billion-dollar fortune and clearly Maxima Chan Zuckerberg is already quite the daddy's girl!

The Facebook founder shared a touching photograph of his newborn baby daughter on Tuesday. 

Captioned simply 'full of joy with little Max', the picture shows an emotional Zuckerberg nestling the tiny baby girl in his hand as they look into each other's eyes.

The father and daughter pair appear to be lying on a carpeted floor, with a pillow propped behind the 31-year-old billionaire. Baby Max's discarded onesie is just in shot. 

The image, which shows a happy-looking Max kicking her feet in the air while wearing just a diaper, may suggest the Silicon Valley tycoon has already got his hands dirty and done his first baby changing. 

The post has already earned thousands of Likes and comments after being shared on Facebook. Zuckerberg shared it alongside a photo of the family's dog Beast wearing a comedy Hanukkah costume. The Jewish festival began on Sunday December 6 and ends on Monday evening. 

In replies to comments on the pictures, notoriously private Zuckerberg gave some small insights into his new family life. 

'Everyone is doing great', he told one fan who asked how his wife Priscilla and his daughter were getting on. 

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Joy: Mark Zuckerberg shared the emotional picture of baby Max on Tuesday on Facebook

New addition: Mark Zuckerberg and his wife Priscilla Chan welcomed their baby daughter Max into the world earlier this month with a touching photo left. On Tuesday they shared a new picture of the little girl alongside one of the family dog Beast, pictured right

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Thousands of well-wishers - including many new parents who shared their own pictures from around the world - flooded the page to offer their support. 

'Nothing like the joy of a baby', as one commentator said. 

However, not all the feedback was glowing praise for the social media mogul. Some moms took to the comment section to urge him to put a blanket under his child so she wouldn't be lying directly on 'germ-filled' carpet.

'Put a blanket on the floor!!! Nasty germs for baby!!!!' one woman implored. 

The post sparked a long running discussion about hygiene and babies - with most concluding a little free reign is good for them.

Maxima inspired one of America's biggest philanthropic pledges on her arrival into the world.  

In a Facebook post entitled, 'A letter to our daughter', the couple revealed plans to set up an initiative to support good causes and pledged to donate 99% of their Facebook shares - currently valued at $46 billion - to its work.

That would leave them with $460 million for themselves and their new child - based on Facebook's current valuation - plus any other private wealth held by the couple or future earnings beyond the social network. 

The letter was accompanied with a picture of the proud new parents tenderly holding their newborn wrapped in a Aden And Anais swaddle cloth covered in cartoon caterpillars.

'Dear Max,' the 2234 word post read. 'Your mother and I don't yet have the words to describe the hope you give us for the future. Your new life is full of promise, and we hope you will be happy and healthy so you can explore it fully. You've already given us a reason to reflect on the world we hope you live in.' 

The couple announced Priscilla's pregnancy on Facebook earlier this year - acknowledging their long struggle with fertility issues and revealing they had suffered several miscarriages before conceiving their healthy little girl.

They used the open letter as an opportunity to describe 'the world we hope she grows up in'. 

'Like all parents, we want you to grow up in a world better than ours today,' it says. 'While headlines often focus on what's wrong, in many ways the world is getting better. Health is improving. Poverty is shrinking. Knowledge is growing. People are connecting. Technological progress in every field means your life should be dramatically better than ours today.

'We will do our part to make this happen, not only because we love you, but also because we have a moral responsibility to all children in the next generation.

'We believe all lives have equal value, and that includes the many more people who will live in future generations than live today. Our society has an obligation to invest now to improve the lives of all those coming into this world, not just those already here.' 

Later in the letter, the couple outlined how they intend to make such a difference. 

'As you begin the next generation of the Chan Zuckerberg family, we also begin the Chan Zuckerberg Initiative to join people across the world to advance human potential and promote equality for all children in the next generation. Our initial areas of focus will be personalized learning, curing disease, connecting people and building strong communities.

'We will give 99% of our Facebook shares -- currently about $45 billion -- during our lives to advance this mission,' the letter says. 'We know this is a small contribution compared to all the resources and talents of those already working on these issues. But we want to do what we can, working alongside many others.

Proud: Mark Zuckerberg and his wife have been open about their pregnancy - announcing it in a Facebook post with an emotional explanation of their struggles with infertility. This picture with their dog Beast accompanied the post

'We'll share more details in the coming months once we settle into our new family rhythm and return from our maternity and paternity leaves. We understand you'll have many questions about why and how we're doing this.'  

Zuckerberg has been more public with the pregnancy and birth of his daughter than many would have previously expected.

The CEO announced he would be taking two months paternity leave following Max's birth and outlined a new proposal to give Facebook fathers the option of four months leave on full pay. 

He said he made the 'personal decision' to take time off after reading studies that show 'when working parents take time to be with their newborns, outcomes are better for the children and families'. 

Back in August when they announced they were expecting their first child they also revealed they had suffered several heartbreaking miscarriages along the way. 

In a candid Facebook post, the couple detailed the heartache and loneliness they had experienced as a result. 

'We want to share one experience to start. We've been trying to have a child for a couple of years and have had three miscarriages along the way.' 

'You feel so hopeful when you learn you're going to have a child. You start imagining who they'll become and dreaming of hopes for their future. You start making plans, and then they're gone. It's a lonely experience,' the couple said. 

'Most people don't discuss miscarriages because you worry your problems will distance you or reflect upon you, as if you're defective or did something to cause this. So you struggle on your own.

'In today's open and connected world, discussing these issues doesn't distance us; it brings us together. It creates understanding and tolerance, and it gives us hope.

'When we started talking to our friends, we realized how frequently this happened -- that many people we knew had similar issues and that nearly all had healthy children after all.

'We hope that sharing our experience will give more people the same hope we felt and will help more people feel comfortable sharing their stories as well.' 

Zuckerberg and Chan met at a party in Harvard in Zuckerberg's sophomore year and began dating in 2003. 

They married in his backyard in 2012 when Chan also celebrated her graduation from medical school.  

Great expectations: The couple have vowed to use their riches to improve life for future generations including their daughter Max