let y = ln(sqrt(2x-8)/(9x+5))

=> y = ln(sqrt(2x - 8) - ln(9x + 5)

=> y = (1/2)ln(2x - 8) - ln(9x + 5) ...........now we will take the derivative

=> y' = (1/2)*[1/(2x - 8)]*2 - 1/(9x + 5) * 9

=> y' = 1/(2x - 8) - 9/(9x + 5)

let y = ln(6x-11)/x((x^2+1)^(1/3))2. ln(6x-11)/x((x^2+1)^(1/3))

by the quotient rule (and chain rule and product rule, we'll use them all)

y' = {[x((x^2+1)^(1/3))]*6/(6x - 11) - ln(6x - 11)*[(x^2 + 1)^(1/3) + (x/3)(x^2 + 1)^(-2/3) * 2x]}/[x((x^2+1)^(1/3))]^2

now we simplify this monstrosity

y ' = {[6x((x^2+1)^(1/3))]/(6x - 11) - ln(6x - 11)(x^2 + 1)^(-2/3) * (x^2 + 1 + (2x^2)/3}/[x((x^2+1)^(1/3))]^2

...and so on...

i'm really not in the mood to simplify this further, good luck with it