Differentiate $\displaystyle y=log \frac{x+1}{x+4}$
1. Is $\displaystyle \log$ meant to be the same as $\displaystyle \ln$ ?
If so
$\displaystyle y=\log (x+1) - \log( x+4) ~\implies~ y'=\dfrac1{x+1} - \dfrac1{x+4} = $$\displaystyle \dfrac{(x+4)-(x+1)}{(x+4)(x+1)}= \dfrac3{(x+4)(x+1)}$
2. If log means $\displaystyle \log_{10}$ then you have transform these logarithms into natural logarithms using the base change formula.