Q.1 (A)(iii) If y = log(e^x/x²), then dy/dx =? A. (2-x)/x B. (x-2)/x C. (e-x)/ex D. (x-e)/ex

Answer: (b) (x-2)/x y = log e^x - log x² = x - 2log x. Therefore dy/dx = 1 - 2/x = (x-2)/x.

If \(y = \log\left(\dfrac{e^x}{x^2}\right)\), then \(\dfrac{dy}{dx} = ?\)

Q.1 (A)(iii) If \(y = \log\left(\dfrac{e^x}{x^2}\right)\), then \(\dfrac{dy}{dx} = ?\)

A. \(\dfrac{2-x}{x}\)

B. \(\dfrac{x-2}{x}\)

C. \(\dfrac{e-x}{ex}\)

D. \(\dfrac{x-e}{ex}\)

Doubtly Asked 29 Oct 2026 Board exam · March 2024 hsc 12th Save WhatsApp Report

Best answer

Answer: (b) \(\dfrac{x-2}{x}\)

\(y = \log e^x - \log x^2 = x - 2\log x\). Therefore \(\dfrac{dy}{dx} = 1 - \dfrac{2}{x} = \dfrac{x-2}{x}\).

Doubtly AI · 29 Oct 2026 AI-verified · Nov 2026 Report

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