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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. \(\frac {dy}{dx} = \frac {10x^{2/3}}{3} - \frac {8x^{2/3}}{3}\)
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Correct Answer: Option 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

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

There is an explanation video available below.


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Explanation Video

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