(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Determine the domain and find the derivative

f(x) = ln|(x+2)/(x^{3}- 1)|

2. Relevant equations

3. 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 seperate 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.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Derivatives of ln including Absolute Value

**Physics Forums | Science Articles, Homework Help, Discussion**