Differentiate \((x^2 - \frac{1}{x})^2\) with respect to \(x\).

  • A \(4x^2 - 4x - \frac{2}{x}\)
  • B \(4x^2 - 2 + \frac{2}{x^3}\)
  • C \(4x^2 - 2 - \frac{2}{x^3}\)
  • D \(4x^2 - 3x + \frac{2}{x}\)
jamb 2006mathematics

The correct answer is C. \(4x^2 - 2 - \frac{2}{x^3}\)

\[y = \left(x^2 - \frac{1}{x}\right)^2\]

\[y = \left(x^2 - \frac{1}{x}\right)\left(x^2 - \frac{1}{x}\right)\]

\[y = x^4 - x - x + \frac{1}{x^2}\]

\[y = x^4 - 2x + \frac{1}{x^2}\]

\[y = x^4 - 2x + x^{-2}\]

\[\frac{dy}{dx} = 4x^2 - 2 - 2x^{-3}\]

\[= 4x^2 - 2 - \frac{2}{x^3}\]

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