Answer
y' = -$ \frac{1}{x(lnx)^{2}}$
Work Step by Step
y = $\frac{1}{lnx}$
Recall for this problem: Quotient Rule
Differentiate:
y' = ($\frac{1}{lnx}$)'
y' = $\frac{lnx(1)' - 1(lnx)'}{(lnx)^{2}}$
y' = $\frac{0 - \frac{1}{x}}{(lnx)^{2}}$
y' = $\frac{-\frac{1}{x}}{(lnx)^{2}}$
y' = -$ \frac{1}{x(lnx)^{2}}$
