Use Logarithmic Differentiation to find $\frac{d}{dx} (x^{{x}^{x}})$ at $x=1$ How do  do this?

Use Logarithmic Differentiation to find $\frac{d}{dx} (x^{{x}^{x}})$ at $x=1$.


Hint: $x^{x}=y$ . take a log of both side  you get $x$log$x$=log$y$. take derivative. then  you will get
$\dfrac{d}{dx} (x^{x})$$ = y'= x^{x}($log$x+1$) . Now write $x^{x^{x}}=y$ take log of both side . then $x^{x}$log$x=$log$y$. Now take derivative. I hope you can do the rest.
