Thank you for your post, I'm happy to provide some information here.
Taxes are calculated automatically within Shopify, but you can override these tax rates for greater control over the taxes that you charge. In your case, you will want to set up taxes as normal for the non-exempt item (you can find instructions to do so as well as country-specific links in this help document). For the VAT-exempt product, you can create a tax override of 0% and apply it to that product in the applicable countries. Check out this help document for more information and the instructions for setting up a tax override.
Please let me know if you have any other questions!
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