[jQuery] Target secon

[skube]

I have a simple problem, but for some reason I can't figure out the
jQuery way to do it. Basically, all I want is to target every child
(except the first one) of a group of elements.

Say, for example, one has multiple divs:
<div class="myDiv">
  <p>First</p>
  <p>Second</p>
  <p>Third</p>
</div>
<div class="myDiv">
  <p>First</p>
  <p>Second</p>
  <p>Third</p>
</div>

And say, I want to hide every <p> except the first one of every <div>:
<div class="myDiv">
  <p>First</p>
</div>
<div class="myDiv">
  <p>First</p>
</div>

I thought I could simply:
$('div.myDiv p').not(':first').hide();

But that only acts on the first <div>  and not all of them resulting
in:
<div class="myDiv">
  <p>First</p>
</div>
<div class="myDiv">
  <p>First</p>
  <p>Second</p>
  <p>Third</p>
</div>

So I thought I have to act on each <div>:
$('div.myDiv').each(function(){
 $('p').not(':first').hide();
})

But that only acts on the first div as well. I know it's something
fundamental I missing, but for the life of me can't see it...