DUE IN 2 HOURS (at 12AM eastern)
1. ln(sqrt(2x-8)/(9x+5))
2. ln(6x-11)/x((x^2+1)^(1/3))
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