Differentiate the function y = [3]{x²(2x - x²)

Correct Answer is : dydx=10x2/33−8x5/33dy/dx = {10x²/3}}{3} - {8x^{5/3}}{3}dxdy=310x2/3−38x5/3

dy/dx = {10x^{5/3}}{3} - {8x²/3}}{3}

dy/dx = {10x²/3}}{3} - {8x^{5/3}}{3}

dy/dx = {10x^{5/3}}{3} - {8x^{5/3}}{3}

dy/dx = {10x²/3}}{3} - {8x²/3}}{3}

Correct Answer is : dydx=10x2/33−8x5/33dy/dx = {10x²/3}}{3} - {8x^{5/3}}{3}dxdy=310x2/3−38x5/3

Test Index

JAMB Mathematics 2023 Paper

Question : 23

Total: 80

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

Solution:

Concept:

Rewrite the radical as a fractional exponent, expand the product, then differentiate each term using the power rule.

Explanation:

Start with

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

Write

\sqrt[3]{x^2}

x^{2/3}

y = x^{2/3}(2x - x^2)

Expand the brackets:

y = 2x^{2/3+1} - x^{2/3+2}

Simplify the exponents:

y = 2x^{5/3} - x^{8/3}

Differentiate with respect to

x

\frac{dy}{dx} = 2 \cdot \frac{5}{3}x^{5/3-1} - \frac{8}{3}x^{8/3-1}

This simplifies to

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

Therefore, the correct option is B.

Answer:

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

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