Explain how currency depreciation can impact domestic output in the short and long term.

When a country's currency depreciates, it loses value relative to the currency of other nations.  According to today's valuation, one Euro can purchase $1.09 in United States Dollars (USD).  If the USD were to further depreciate, the exchange rate would give a further advantage to the Euro because it could be used to purchase a larger amount of dollars.  Why is this relevant to trade?  There is a relationship between the value of currency and the value of a nation's product for exportation.
When a entities in foreign countries seek to purchase goods, they seek the best value.  If their currency has a higher exchange rate compared to a second country, they will exchange currencies in order to make a purchase.  This higher exchange rate creates an incentive for the stronger nation to import goods, while the economy with the weaker currency has an incentive to export goods.
When an economy has a greater exportation rate, they will be producing more products to meet this demand.  Although this marks a short term increase in domestic output, the effects may not be the same in the long term.  If an item requires a commodity of foreign origin to complete the manufacturing process, the higher exchange rate required to purchase this commodity will eventually cause an increase in the price of the product.  The increase in price may decrease the demand for the product, leading to decreased production.
https://www.bea.gov/help/faq?faq_id=498

https://www.investopedia.com/terms/c/currency-appreciation.asp