Changing font awesome icon onclick function

function arata_ascunde(button) {
   var x = $('#showhide');
   $(button).find('i').remove();
   if ($(button).text().trim() == 'Show') {
     $(button).html($('<i/>',{class:'fa fa-eye-slash'})).append(' Hide');
     x.fadeIn();
    }
    else {
      $(button).html($('<i/>',{class:'fa fa-eye'})).append(' Show');
      x.fadeOut();
    }
}
<link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/4.7.0/css/font-awesome.min.css" rel="stylesheet"/>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
    <button onclick="arata_ascunde(this);" style="align:right;font-size:13px"
            class="btn btn-info " id="show_hide_bt" style="background-color:#00b0ff;">
        <i class="fa fa-eye"></i> Show
    </button>
    <div id="showhide" style="background-color:red;width:100px;height:100px;margin:10px;display:none;"></div>


document.querySelector('button').addEventListener('click', function() {
  const icon = this.querySelector('i');
  const text = this.querySelector('span');

  if (icon.classList.contains('fa-eye')) {
    icon.classList.remove('fa-eye');
    icon.classList.add('fa-eye-slash');
    text.innerHTML = 'Hide';
  } else {
    icon.classList.remove('fa-eye-slash');
    icon.classList.add('fa-eye');
    text.innerHTML = 'Show';
  }
});
<link href="https://cdnjs.cloudflare.com/ajax/libs/skeleton/2.0.4/skeleton.min.css" rel="stylesheet" />
<link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/4.7.0/css/font-awesome.min.css" rel="stylesheet" />

<button><i class="fa fa-eye"></i> <span>Show</span></button>


Since you have inserted Jquery. You can do this via Jquery easily.

<button style="align:right;font-size:13px" class="btn btn-info" id="show_hide_bt" style="background-color:#00b0ff;"><i 
class="fa fa-eye"></i> Show</button>

Now Jquery code for this is

$("#show_hide_bt").click(function(event) {
    $(this).find('i').toggleClass('fa-eye-slash');
});

If you want to remove the fa-eye class then you can chain another toggleClass or add this again

$(this).find('i').toggleClass('fa-eye');

Or add this in single line. Comment if this doesnot help

$(this).find('i').toggleClass('fa-eye-slash').toggleClass('fa-eye');