1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook