Derivative of $x^{x^x}$
Solution 1:
What if you represented your function as
$f(x) = x^{x^x} = \exp(x^x \cdot \ln x) = \exp(\,\exp(x\ln(x)) \cdot \ln x \, )$
Then you can apply the chain rule with the product rule.
Solution 2:
It's $z=x^y$ not $z = y^x$ so $z= y\ln x$ not $z = x\ln y$