Derivative of $(log (x))^{x}$

Question

How can we calculate the value of $ \frac{dy}{dx} (log (x))^{x}$

I tried doing it the following way :

Let $ y= (\log (x))^{x} $

$ \log y = x \log \log (x)$

Then differentiating both sides with respect to $x$ but its not working.

Answer 1

$\log y=x\log \log x$ Differentiate both sides with respect to $x$ you get

$y'/y=\log \log x + x \frac{1}{\log x} \frac{1}{x}$