"She sleeps through most of the day except for feeds and has been most obedient and well behaved! Ha ha ha," Amitabh posted on his blog Bigb.bigadda.com.
"The moments spent with her even though one encounters shut eyes, are the most pleasant and fulfilling, but what after. I think there is an indication here to take up vocations that one has always wanted to pursue - that music lesson, language ... reading to catch up...and on," he posted.
The 69-year-old also thanked his fans for showering their love and suggestion for her 'naam karan' (naming ceremony).
"To all those that have sent and continue to send names for the 'little one', gracious gracious thanks ... we will select soon," he posted on the micro-blogging site Twitter.
Aishwarya Rai gave birth to her and husband Abhishek Bachchan's first child Nov 16.