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

Answer: B. x-2/x Answer: (b) x-2/x Using the laws of logarithms, y=log e^x-log x²=x-2log x . Hence dy/dx=1-2/x=x-2/x .

If \(y=\log\left(\frac{e^x}{x^2}\right)\) then \(\frac{dy}{dx}\) = _____.

Q.1 (A) (ii) If \(y=\log\left(\frac{e^x}{x^2}\right)\) then \(\frac{dy}{dx}\) = _____.

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

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

C. \(\frac{e-x}{e^x}\)

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

Doubtly Asked 28 Oct 2026 Board exam · March 2026 hsc 12th Save WhatsApp Report

Best answer

Answer: B. \(\frac{x-2}{x}\)

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

Using the laws of logarithms, \(y=\log e^x-\log x^2=x-2\log x\). Hence \(\frac{dy}{dx}=1-\frac{2}{x}=\frac{x-2}{x}\).

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

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