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## Homework Statement

Determine the domain and find the derivative

f(x) = ln|(x+2)/(x

^{3}- 1)|

## Homework Equations

## The Attempt at a Solution

We can factor x

^{3}- 1 = (x-1)(x

^{2}) + x + 1)

From this we know that x ≠ 1 or -2 because 1 would be undefined at -2 would cause the function to be ln 0 which is not possible.

Domain = {x[itex]\inℝ[/itex], x ≠ 1,-2}

f(x) = ln(x+2) - ln(x

^{3}- 1)

= ln(x+2) - ln[(x-1)(x

^{2}) + x + 1)]

= ln(x+2) - ln(x-1) - ln(x

^{2}) + x + 1)

f'(x) = 1/(x+2) - 1/(x-1) -(2x+1)/(x

^{2}) + x + 1)

This is where i stopped but i know that there is an absolute value so I'm not sure if i have to find when x is positive and when x is negative and then find the separate derivatives. Please help me figure out if up to here is fine or if i have to keep going and if i do have to keep going, how would i go about finding the derivative? Thank you.