Q.1 (A) (ii) If y=e^(log x) then dy/dx= _____. A. 1/x B. 1/2 C. frace^(log x)x D. 0

Chapter: Differentiation· Mathematics & Statistics (Commerce) Part 1

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

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

A. \(\frac{1}{x}\)

B. \(\frac{1}{2}\)

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

D. 0

Doubtly Asked 29 Oct 2026 Board exam · July 2025 hsc 12th Save WhatsApp Report

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Answer: (c) \(\frac{e^{\log x}}{x}\)

By the chain rule, \(\frac{dy}{dx}=e^{\log x}\cdot\frac{d}{dx}(\log x)=\frac{e^{\log x}}{x}\). (Since \(e^{\log x}=x\), this value equals 1; option (a) \(\frac{1}{x}\) is not equal to 1, so (c) is the only correct choice.)

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

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

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