# If f(x) = log x2, where x > 1 find derivative of f(x)

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If f(x) = log x2, where x > 1 find derivative of f(x)
1. $\rm \frac{2}{x^2}$
2. $\rm \frac{1}{x}$
3. $\rm \frac{2}{x}$
4. $\rm \frac{1}{x^2}$

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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 = xn, then f'(x) = nxn - 1

Calculation:

f(x) = log x2, 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) = $\rm \frac{2}{x}$