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Differentiate \(\frac{6x^3 - 5x^2 + 1}{3x^2}\) with respect to x

Mathematics
JAMB 1997

Differentiate \(\frac{6x^3 - 5x^2 + 1}{3x^2}\) with respect to x
  • A. \(\frac{2 + 2}{3x^3}\)
  • B. 2 + \(\frac{1}{6x}\)
  • C. 2 - \(\frac{2}{3x^3}\)
  • D. \(\frac{1}{5}\)
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Correct Answer: Option C
Explanation
\(\frac{6x^3 - 5x^2 + 1}{3x^2}\)

let y = 3x2

y = \(\frac{6x^3}{3x^2}\) - \(\frac{6x^2}{3x^2}\) + \(\frac{1}{3x^2}\)

Y = 2x - \(\frac{5}{3}\) + \(\frac{1}{3x^2}\)

\(\frac{dy}{dx}\) = 2 + \(\frac{1}{3}\)(-2)x-3

= 2 - \(\frac{2}{3x^3}\)

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