Differentiate the function y = \(\sqrt[3]{x^2}(2x - x^2)\)
MATHEMATICS
JAMB 2023
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: D. \(\frac {dy}{dx} = \frac {10x^{2/3}}{3} - \frac {8x^{2/3}}{3}\)
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
\(\therefore \frac {dy}{dx} = \frac {10x^{2/3}}{3} - \frac {8x^{5/3}}{3}\)
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