Question

Find derivative using the power rule
cube root of X - cube root of X^2

Answer 1

\[\sqrt[3]{x}=x^{\frac{1}{3}}\] and
\[\sqrt[3]{x^2}=x^{\frac{2}{3}}\] so now can use power rule

Answer 2

\[f(x)=x^{\frac{1}{3}}-x^{\frac{2}{3}}\]
\[f'(x)=\frac{1}{3}x^{\frac{1}{3}-1}-\frac{2}{3}x^{\frac{2}{3}-1}\]

Answer 3

\[f'(x)=\frac{1}{3}x^{-\frac{2}{3}}-\frac{2}{3}x^{-\frac{1}{3}}\]

Answer 4

and finally
\[f'(x)=\frac{1}{3\sqrt[3]{x^2}}-\frac{2}{3\sqrt[3]{x}}\]

Answer 5

back in radical form

Answer 6

hope all the gory details were complete and clear

Answer 7

and correct!

Answer 8

I'm sure it was. I'd hate to see you go through all that trouble for nothing