Is correct say : " What did you did lately ? "

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I would say : "What HAVE YOU been doing lately?"

( "lately" as in recent times, not so long ago)

Thank you kittie ! miau-prrrrRR

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when we use simple past tense in a question and negative forms we use base form of the verb V1 in sentences.. 
what did you do? 
but we use the Present Perfect (have/has+V3) with unspecific expressions such as: ever, never, once, many times, several times, before, so far, already, yet, lately..etc 

what have you done lately?

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Jenny-michu, you forgot about inversion:

"what have you been doing"

^__^

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Is it correct if I say '...?' 

No, it isn't correct. The right way to say is : What did you do earlier? 


Positive. I DID it earlier. (DID is the past of DO, in the positive sentences we need to change the verb into the past form). 

Negative. I didn't do it earlier. ( DIDN'T is the auxiliary, and DO is the verb without changes, because in negative sentences the verb remains the same). 

Question: DID you DO it earlier? (DID is the auxiliary and DO the verb without changes).

Answer

What did you do*