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WAEC Further Mathematics 2022 Paper

Question : 12

Total: 45

Differentiate

\;\frac{5x^{3}+x^{2}}{x}

, x ≠ 0 with respect to x.

Solution:

Concept:

Simplify the given rational expression by dividing each term by

x

, then differentiate term by term.

Explanation:

Let

y = \frac{5x^{3}+x^{2}}{x}

Divide each term in the numerator by

x

y = \frac{5x^{3}}{x} + \frac{x^{2}}{x} = 5x^{2} + x

Differentiate with respect to

x

\frac{dy}{dx} = \frac{d}{dx}(5x^{2}) + \frac{d}{dx}(x) = 10x + 1

This corresponds to option A.

Answer:

10x + 1

(Option A).

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