Once an Analytic Entry is created, you would need to manually update the cost, you just edit the entry.

If you want to preserve the original cost, but show the replacement, you would enter two manual entries - the first to reverse the original and the second to record the correct price.

If your prices are changing AFTER you have Invoiced, those changes would normally result in an entry with a different amount for your NEXT Invoice.

Changing costs after an Invoice has been issued is problematic, the Invoice is the LAST thing that happens when you are ready to recognize revenue and calculate cost of goods.