Simplifying the derivative of $x^{\frac{2}{3}} \cdot (6-x)^{\frac{1}{3}}$ $$x^{\frac{2}{3}} \cdot (6-x)^{\frac{1}{3}}$$
So I get:
$$-x^{\frac{2}{3}} \cdot \frac{1}{3} (6-x) ^{\frac{-2}{3}} + (6-x) ^{\frac{1}{3}} \cdot \frac{2}{3} x ^ {\frac{-1}{3}}$$
How does one go about simplifying this?
I guess I can pull out common terms like this:
$$\frac{1}{3} x ^{-\frac{1}{3}} (6-x)^{\frac{-2}{3}} ( -x + (6-x) \cdot 2)$$
Is that right?


Pulling out this common factor is fine. We can simplify the last expression slightly more and obtain
  \begin{align*}
\color{blue}{-x^{\frac{2}{3}}}&\color{blue}{ \cdot \frac{1}{3} (6-x) ^{-\frac{2}{3}} + (6-x) ^{\frac{1}{3}} \cdot \frac{2}{3} x ^ {-\frac{1}{3}}}\\
&=\frac{1}{3}x^{-\frac{1}{3}}(6-x)^{-\frac{2}{3}}(-x+(6-x)2)\\
&=\frac{1}{3}x^{-\frac{1}{3}}(6-x)^{-\frac{2}{3}}(12-3x)\\
&\,\,\color{blue}{=x^{-\frac{1}{3}}(6-x)^{-\frac{2}{3}}(4-x)}
\end{align*}

