Find the derivative of x^(1/x).

Question

Can someone show me steps for this problem...I go round in circles

Answer 1

y = x^(1/x)
ln y = 1/x ln x
1/y y' = -1/x^2 lnx + 1/x * 1/x
1/y y' = 1/x^2 (1-lnx)
y' = x^(1/x - 2)(1 - lnx)