Question

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. \(\rm \frac{1}{x^2}\)

Answer 1

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) = nx^{n - 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) = \(\rm \frac{2}{x}\)