Question

How do you find the derivative `y=ln(9x)/(1+x)`?

Answer 1

The answer is: `y'=(1+x-xln9x)/(x(1+x)^2)`.

Using the quotient rule and the chain rule:

`y'=(1/(9x)* 9*(1+x)-ln9x*1)/(1+x)^2=((1+x)/x-ln9x)/(1+x)^2=`

`=(1+x-xln9x)/(x(1+x)^2)`.