Correct Answer: Option D

Explanation

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

Let u = 4x\(^3\) - 2x.

\(\frac{\mathrm d}{\mathrm d x} (\log (4x^3 - 2x)) = (\frac{\mathrm d}{\mathrm d u})(\frac{\mathrm d u}{\mathrm d x})\)

\(\frac{\mathrm d}{\mathrm d u} (\log u)\) = \(\frac{1}{u}\)

\(\frac{\mathrm d u}{\mathrm d x} = 12x^2 - 2\)

\(\therefore \frac{d}{dx} [\log (4x^3 - 2x)] = \frac{12x^2 - 2}{u}\)

= \(\frac{12x^2 - 2}{4x^3 - 2x}\)

There is an explanation video available below.

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