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JAMB Mathematics 2012 Paper

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Question : 29

Total: 48

If y = x² -

\frac{1}{x}

\frac{\delta y}{\delta x}

2x - $\frac{1}{x^2}$
2x + x²
2x - x²
2x + $\frac{1}{x^2}$

Solution:

Concept:

Rewrite

\frac{1}{x}

as a power of

x

, then differentiate each term using the power rule.

Explanation:

Given

y = x^2 - \frac{1}{x}

.

Rewrite:

y = x^2 - x^{-1}

.

Differentiate term by term:

\frac{d}{dx}(x^2) = 2x

.

\frac{d}{dx}(-x^{-1}) = +x^{-2}

.

So

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

.

Since

x^{-2} = \frac{1}{x^2}

, we get:

\frac{dy}{dx} = 2x + \frac{1}{x^2}

.

Answer:

\frac{dy}{dx} = 2x + \frac{1}{x^2}

Correct option: D.

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