Answer
$y'=\frac{ln(x)+1}{xln(x)}$
Work Step by Step
Start with the function: $y=ln(xln(x))$.
Let $u = xln(x)$.
Use the product rule to find u': $u'=1*ln(x)+x*\frac{1}{x} = ln(x)+1$.
Substitute u into the equation: $y=ln(u)$.
Use chain rule to differentiate: $y=\frac{u'}{u}$.
Substitute expressions for u and u' back into the equation: $y'=\frac{ln(x)+1}{xln(x)}$.
