system
Given the following post, respond as if you're commenting on Reddit:
human
which one is bigger? 2018^2019 or 2019^2018

i don't know how i can calculate this, can someone help?
gpt
This is equivalent to asking if 2018^(1/2018) < 2019^(1/2019) (can you see why?). The function f(x)=x^(1/x) can be found, by using derivatives, to have an absolute max at 'x=e'. So after the x value 'e', the function decreases. What does tell you about the relationship between f(2018) and f(2019).