How do I select the first div in these divs (the one with id=div1) using first child selectors?
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Use the :first-child selector.
In your example...
$('div.alldivs div:first-child')
This will also match any first child descendents that meet the selection criteria.
While :first matches only a single element, the :first-child selector can match more than one: one for each parent. This is equivalent to :nth-child(1).
For the first matched only, use the :first selector.
Alternatively, Felix Kling suggested using the direct descendent selector to get only direct children...
$('div.alldivs > div:first-child')