# Thread: Differentiation - Quotient Rule.

1. ## Differentiation - Quotient Rule.

I'm working on an assignment and the probelm asks to differentiate h(x) = (x^1/3)/(x^3+1)

I keep getting (x^3 + 1 - 3x^(7/3)) / (3x^(2/3)(x^3 + 1)^2

However, the answer in the back of the book is: (1 - 8x^3) / (3x^(2/3)(x^3 + 1)^2

I've reworked this problem several times and i cannot figure out what I'm doing wrong. I would appreciate any help. Thanks!

2. ## Re: Differentiation - Quotient Rule.

Originally Posted by brandito239
I'm working on an assignment and the probelm asks to differentiate h(x) = (x^1/3)/(x^3+1)
$\displaystyle {\left( {\frac{{{x^{\frac{1}{3}}}}}{{{x^3} + 1}}} \right)^\prime } = \frac{{\frac{1}{3}{x^{\frac{{ - 2}}{3}}}({x^3} + 1) - {x^{\frac{1}{3}}}(3{x^2})}}{{{{\left( {{x^3} + 1} \right)}^2}}} = \frac{{({x^3} + 1) - 3x(3{x^2})}}{{3{x^{\frac{2}{3}}}{{\left( {{x^3} + 1} \right)}^2}}}$

3. ## Re: Differentiation - Quotient Rule.

I still don't understand how you were able to simplify x^(1/3)(3x^2) to 3x(3x^2).

4. ## Re: Differentiation - Quotient Rule.

Originally Posted by brandito239
I still don't understand how you were able to simplify x^(1/3)(3x^2) to 3x(3x^2).
You need to study very basic algebra.
No one can do calculus, without a complete grounding in basic algebraic operations.

5. ## Re: Differentiation - Quotient Rule.

I certainly hope you're not representative of every MHF expert/helper on this forum, because if you are, you really make mathematicians look like horrible people. I do agree I need to brush up on all of my math skills. I know I'm far from being a math expert, which is why I came to this website. I was hoping someone who is an expert could offer some real guidance and not just give a condescending and rude response.

6. ## Re: Differentiation - Quotient Rule.

Originally Posted by brandito239
I still don't understand how you were able to simplify x^(1/3)(3x^2) to 3x(3x^2).
Multiply the top and bottom by \displaystyle \displaystyle \begin{align*} 3x^{\frac{2}{3}} \end{align*}.

7. ## Re: Differentiation - Quotient Rule.

Originally Posted by Prove It
Multiply the top and bottom by \displaystyle \displaystyle \begin{align*} 3x^{\frac{2}{3}} \end{align*}.
Thanks so much! I appreciate the help!