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WAEC Further Mathematics 2017 Paper

Question : 26

Total: 40

Differentiate

\; \frac{5x^{3}\;+\;x^{2}}{x}, x \neq 0

with respect to x.

Solution:

Concept:

Simplify the rational expression by dividing each term by

x

, then differentiate term by term using the power rule.

Explanation:

The given expression is

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

. Instead of applying the quotient rule, divide each term of the numerator by

x

This gives

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

Now differentiate

5x^2 + x

with respect to

x

\displaystyle \frac{d}{dx}(5x^2) = 5 \cdot 2x = 10x

\displaystyle \frac{d}{dx}(x) = 1

Therefore,

\displaystyle \frac{d}{dx}\left(\frac{5x^3 + x^2}{x}\right) = 10x + 1

Answer:

10x + 1

This matches option A.

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