If you are asking which United States president was the first to die at all, the answer is George Washington. He was, of course, the first president and was also the first to die. Washington was president from 1789 to 1797 and he only lived a short time after leaving office. He died in 1799, while John Adams was governing as the second president of the US.
If you are asking about the first president to actually die while he was president, the answer would be William Henry Harrison. Harrison was the 9th president of the United States. He was elected in 1840 and took office in 1841. He died after serving only one month in office. He is the president who served for the shortest time.