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

A.

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

B.

\(\frac{43x^2 - 2x}{7x}\)

C.

\(\frac{4x^2 - 2}{7x + 6}\)

D.

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

Correct answer is D

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

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

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

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

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

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

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