Find the derivative of \(3x^{2} + \frac{1}{x^{2}}\)
FURTHER MATHEMATICS
WAEC 2008
Find the derivative of \(3x^{2} + \frac{1}{x^{2}}\)
- A. \(6x + 2x^{2}\)
- B. \(6x + \frac{1}{2x}\)
- C. \(6x - \frac{2}{x^{3}}\)
- D. \(6x - \frac{1}{2x}\)
Correct Answer: C. \(6x - \frac{2}{x^{3}}\)
Explanation
\(y = 3x^{2} + \frac{1}{x^{2}} \equiv y = 3x^{2} + x^{-2}\)
\(\frac{\mathrm d y}{\mathrm d x} = 6x - 2x^{-3}\)
= \(6x - \frac{2}{x^{3}}\)
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