Q.1 (v) If x=e^(x/y) then dy/dx= ____. A. 1-y/x B. 1+y/x C. x-y/xlog x D. x+y/xlog x

Answer: C. x-y/xlog x Answer: (c) x-y/xlog x Taking logarithms, log x=x/y , so y=x/log x . dy/dx=log x-x·1/x/(log x)²=log x-1/(log x)² . Also x-y/xlog x=x-x/log x/xlog x=log x-1/(log x)² . Hence dy/dx=x-y/xlog x .

Chapter: Differentiation· Mathematics & Statistics Part 2

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

Q.1 (v) If \(x=e^{\frac{x}{y}}\) then \(\dfrac{dy}{dx}=\) ____.

A. \(1-\dfrac{y}{x}\)

B. \(1+\dfrac{y}{x}\)

C. \(\dfrac{x-y}{x\log x}\)

D. \(\dfrac{x+y}{x\log x}\)

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

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Answer: C. \(\dfrac{x-y}{x\log x}\)

Answer: (c) \(\dfrac{x-y}{x\log x}\)

Taking logarithms, \(\log x=\dfrac{x}{y}\), so \(y=\dfrac{x}{\log x}\).

\(\dfrac{dy}{dx}=\dfrac{\log x-x\cdot\frac1x}{(\log x)^2}=\dfrac{\log x-1}{(\log x)^2}\).

Also \(\dfrac{x-y}{x\log x}=\dfrac{x-\frac{x}{\log x}}{x\log x}=\dfrac{\log x-1}{(\log x)^2}\). Hence \(\dfrac{dy}{dx}=\dfrac{x-y}{x\log x}\).

Doubtly AI · 29 Oct 2026 AI-generated · not yet verified Report

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

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