How to get child element by index in Jquery?

If you know the child element you're interested in is the first:

 $('.second').children().first();

Or to find by index:

 var index = 0
 $('.second').children().eq(index);

There are the following way to select first child

1) $('.second div:first-child')
2) $('.second *:first-child')
3) $('div:first-child', '.second')
4) $('*:first-child', '.second')
5) $('.second div:nth-child(1)')
6) $('.second').children().first()
7) $('.second').children().eq(0)