The question's a bit old, but since I came across while looking for a similar problem, thought I'd share the solution I went with here - Mutation Observers
In your case, I'd create a mutation observer
var mut = new MutationObserver(function(mutations, mut){
// if attribute changed === 'class' && 'open' has been added, add css to 'otherDiv'
});
mut.observe(document.querySelector(".slide-out-div"),{
'attributes': true
});
The function in mutation observer is called any time an attribute of .slide-out-div is changed, so need to verify the actual change before acting.
More details here on Mozilla's documentation page