Please show the steps and the final answer. Thank you!

ln(x^x) = x ln x, so x^x = e^(x ln x). Now, ln (x^(x^x)) = (x^x) ln x
= (ln x)(e^(x ln x)). Thus, x^(x^x) = e^((ln x)(e^(x ln x))).
Thus, dy/dx = e^((ln x)(e^(x ln x)))*d/dx((ln x)(e^(x ln x)))
=(x^(x^x))*d/dx((ln x)(e^(x ln x))) = (x^(x^x))*((e^(x ln x))/x +
(ln x)*(d/dx(e^x ln x))) = (x^(x^x))*((e^(x ln x))/x +
(ln x)(e^(x ln x))(1 + ln x)) = (x^(x^x))*((x^x)/x +
(x^x)(ln x)(1+ln x)) = (x^(x^x))(x^x)((1/x) + ln x + (ln x)^2).
Hope this helps.