Question

if f(y)=y^6/6lny-y^6/36, find f'(y)

Answer 1

It looks like you have

$f(y)=\dfrac{y^6}{6\ln(y)}-\dfrac{y^6}{36}$

Differentating gives

$f'(y)=\dfrac{6y^5\times6\ln(y)-6y^6\times\frac1y}{(6\ln(y))^2}-\dfrac{6y^5}{36}= -\dfrac{y^5\left(\ln^2(y)-6\ln(y)+1\right)}{6\ln^2(y)}$