Correct Answer - Option 3 :

\(\rm \frac{2}{x}\)
__Concept:__

Chain rule: \(\rm \frac{d}{dx}[f(g(x))]= f'(g(x)) g'(x)\)

If y = log x, then f'(x) = 1/x

And if y = x^{n}, then f'(x) = nx^{n - 1}

__Calculation:__

f(x) = log x^{2}, x > 1

Differentiating with respect to x, we get

⇒ f'(x) = (\(\rm \frac{1}{x^2}\))\(\rm \frac{d x^2}{dx}\)

⇒ f'(x) = \(\rm \frac{2x}{x^2}\)

⇒ f'(x) = \(\rm \frac{2}{x}\)