Find dy/dx, if y = 2/3 x³ - 4/x

Correct Answer is : 2x2 +4x24/x²x24

Correct Answer is : 2x2 +4x24/x²x24

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JAMB Mathematics 2016 Paper

Question : 26

Total: 50

Find

\frac{dy}{dx}

\frac{2}{3}

^3

\frac{4}{x}

Solution:

Concept:

Use power rule for differentiation: if

y = ax^n

, then

\frac{dy}{dx} = anx^{n-1}

Explanation:

Rewrite the given function:

y = \frac{2}{3}x^3 - \frac{4}{x}

Convert the second term to a power:

-\frac{4}{x} = -4x^{-1}

Differentiate each term with respect to

x

\frac{d}{dx}\left(\frac{2}{3}x^3\right) = \frac{2}{3} \cdot 3x^{2} = 2x^2

\frac{d}{dx}\left(-4x^{-1}\right) = -4 \cdot (-1)x^{-2} = 4x^{-2} = \frac{4}{x^2}

Combine the derivatives:

\frac{dy}{dx} = 2x^2 + \frac{4}{x^2}

Answer:

2x^2 + \frac{4}{x^2}

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