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Chain rule problem

  1. Sep 30, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the derivative:

    ( (X^3-1)/(X^3+1) )^1/3

    2. Relevant equations
    d/dx f(g(x)) = f'(g(x)) * g'(x)

    quotient rule x/a x'a-xa'/a^2

    3. The attempt at a solution

    first i used the chain rule and quotient rule to get 1/3 ((x^3-1)/(x^3+1))^-2/3 * ((3x^2(x^3+1) - (x^3-1)3x^2)/(x^3+1)^2)

    canceling some thing out on the second part of the neumerator i ended up with

    1/3 ((x^3-1)/(x^3+1))^-2/3 * ((6x^2)/(x^3+1)^2)

    if i try to simplify more it just get into a hole bunch of nasty fractions... and it just doesn't seem like the right answer, i must have taken a wrong turn some where

    thanks a lot!
  2. jcsd
  3. Oct 1, 2008 #2
    Got the same as you, except on the numerator of the second part it's 6x^2 - 2x^3
    like: 1/3 ((x^3-1)/(x^3+1))^-2/3 * ((6x^2 - 2x^3)/(x^3+1)^2)

    make sure to get your minus sign right in the numerator when doing the quotient rule.
  4. Oct 1, 2008 #3
    is that the final answer? it seems a bit large to be?

  5. Oct 1, 2008 #4
    Is there a rule as to how large answers are allowed to be?

    If you really want to get complicated you can simplify it to [tex] \frac{2x^2}{(x^3-1)^{2/3} (x^3+1)^{4/3}}[/tex]
  6. Oct 1, 2008 #5
    great thanks so much
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