What is the derivative of y=x/lnx? Simpify the answer fully.

y = x/[ln(x)]

Quotient rule:
y' = {ln(x)d/dx[x] - xd/dx[ln(x)]} / {[ln(x)]²}

Take the derivatives:
y' = {ln(x) - x*(1/x)} / {[ln(x)]²}

Simplify:
y' = {ln(x) - 1} / {[ln(x)]²}

Using quotient rule f ` (x) is given by :-

ln x - 1
-----------
(ln x )²