The second sentence is correct ; this is an ellipsis which uses the word "so" or the words "and so", followed by the verb or the first auxiliary verb.
In English, words can sometimes be omitted from a sentence without changing the meaning of the sentence. The words which are omitted are said to be "understood". This type of short form is usually referred to as ellipsis.
source: English Grammar
" The world is changing all the time , and so / so are the words."
The world changes all the time,and so / so do the words.
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