Question

What is the value of ln ⁡\(\frac{3}{x}\)?

(a) ⁡\(\frac{2}{x^3}\)

(b) ⁡\(\frac{-3}{x^3}\)

(c) ⁡\(\frac{-9}{x^3}\)

(d) ⁡\(\frac{9}{x^3}\)

This question was posed to me in final exam.

This question is from Derivatives topic in division Limits and Derivatives of Mathematics – Class 11

Answer 1

The correct answer is (c) ⁡\(\frac{-9}{x^3}\)

For explanation: We use chain rule to find \(\frac{d}{dx}\)(ln ⁡\(\frac{3}{x}\)).

\(\frac{d}{dx}(ln \frac{3}{x}\)) = \(\frac{1}{\frac{3}{x}} \frac{d}{dx}(\frac{3}{x})\)

\(\frac{d}{dx}(ln \frac{3}{x}\)) = \(\frac{3}{x}(-\frac{3}{x^2})\)

\(\frac{d}{dx}(ln \frac{3}{x}\)) = \(\frac{-9}{x^3}\)