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