Differentiate the function y = \(\sqrt[3]{x^2}(2x - x^2)\)

A.

\(\frac {dy}{dx} = \frac {10x^{5/3}}{3} - \frac {8x^{2/3}}{3}\)

B.

\(\frac {dy}{dx} = \frac {10x^{2/3}}{3} - \frac {8x^{5/3}}{3}\)

C.

\(\frac {dy}{dx} = \frac {10x^{5/3}}{3} - \frac {8x^{5/3}}{3}\)

D.

\(\frac {dy}{dx} = \frac {10x^{2/3}}{3} - \frac {8x^{2/3}}{3}\)

Correct answer is B

y = \(\sqrt[3]{x^2(2x - x^2)} = x^{2/3} (2x - x^2)\)

= \(2x^{5/3} - x^{8/3}\)

Now, we can differentiate the function

\(\therefore \frac {dy}{dx} = \frac {10x^{2/3}}{3} - \frac {8x^{5/3}}{3}\)