How you doing is a shortened version of the more formal greeting. How are you doing? The sentence “how you doing?” is a question addressed to a person by another person, commonly in greeting or while being introduced to someone, to be courteous and elicit a response about their general state of mind and how their life is going on.

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What is the Origin of How You Doing?
There is no information about the first use of the phrase how you doing as a greeting. However, this salutation initially appeared in print in the 1940s and was widely used in the 1970s and 1980s. How you doing was a common phrase among New Yorkers of Italian heritage in the late twentieth century.

What is Correct? How You Doing? Or How are You Doing?
Well, how are you doing sounds more professional, and it is the proper way to use it. But how you doing is frequently used in verbal conversations. Hence you can’t say it is wrong English. But this way of using is more into informal communication.
E.g., what’s up? How you doing, bro?

Similar Salutation for How You Doing
What’s up
How’s life
How you been
What’s new with you