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?

We've got to preserve the terms here, and we see that the ordering is mismatched, as in 
$$\frac{d}{dx}(x^{\frac{2}{3}}(6-x)^{\frac{2}{3}})=\frac{2}{3}(\frac{6-x}{x})^{\frac{1}{3}}-\frac{1}{3}(\frac{x}{6-x})^{\frac{2}{3}}$$
Then we can factor out $(\frac{6-x}{x})^{\frac{1}{3}}$ to make the second term much nicer with no powers
Your answer and this one are ultimately the same
