Thread: Two Hard Derivitive Problems

DUE IN 2 HOURS (at 12AM eastern)



1. ln(sqrt(2x-8)/(9x+5))






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

Originally Posted by lmao

1. ln(sqrt(2x-8)/(9x+5))

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)

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

let y = 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

Originally Posted by Jhevon

...

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

Hopefully lmao put the prentices in the correct place.

For some reason I'm guessing not.

Correct me lmao if I am wrong.

I forgot to mention for the second one it says d(y)/d(x) then y="