\(\frac{d}{dx} [\log (4x^3 - 2x)]\) is equal to

  • A \(\frac{12x - 2}{4x^2}\)
  • B \(\frac{43x^2 - 2x}{7x}\)
  • C \(\frac{4x^2 - 2}{7x + 6}\)
  • D \(\frac{12x^2 - 2}{4x^3 - 2x}\)
jamb 2019mathematics

The correct answer is D. \(\frac{12x^2 - 2}{4x^3 - 2x}\)

To find the derivative of \(\log (4x^3 - 2x)\) with respect to \(x\), we use the chain rule.

The derivative is given by:

\(\frac{d}{dx} [\log (4x^3 - 2x)] = \frac{1}{4x^3 - 2x} \cdot \frac{d}{dx} (4x^3 - 2x)\).

Taking the derivative of \(4x^3 - 2x\) with respect to x, we get \(12x^2 - 2\).

So, the expression becomes \(\frac{1}{4x^3 - 2x} \cdot (12x^2 - 2)\). Ther

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