How do you find the maximum value of (ln(x))/x^2

First i derived: That gave me: (1-2ln(x))/x^3

Now i figure x' is zero at: x = 0

or ln(x) = 0,5 = e^0,5

But the correct answer is suppose to be 1/(2e)

What am i doing wrong?

With Kind regards Henry from Sweden