Q.1 (v) If y is a function of x and log(x + y) = xy then the value of (dy/dx) at x = 0 is _____ A. 1 B. -1 C. 2 D. 0

Answer: D. 0 Answer: (d) 0 At x = 0 : log y = 0 , so y = 1 . Differentiating log(x + y) = xy w.r.t. x : 1/x + y(1 + dy/dx) = y + xdy/dx . Put x = 0,\ y = 1 : 1 + dy/dx = 1 , so dy/dx = 0 .

If \(y\) is a function of \(x\) and \(\log(x + y) = xy\) then the value of \(\left(\frac{dy}{dx}\right)\) at \(x = 0\) is _____

Q.1 (v) If \(y\) is a function of \(x\) and \(\log(x + y) = xy\) then the value of \(\left(\frac{dy}{dx}\right)\) at \(x = 0\) is _____

A. 1

B. \(-1\)

C. 2

D. 0

Doubtly Asked 28 Oct 2026 Board exam · July 2025 hsc 12th Save WhatsApp Report

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Answer: D. 0

Answer: (d) 0

At \(x = 0\): \(\log y = 0\), so \(y = 1\). Differentiating \(\log(x + y) = xy\) w.r.t. \(x\): \(\frac{1}{x + y}\left(1 + \frac{dy}{dx}\right) = y + x\frac{dy}{dx}\). Put \(x = 0,\ y = 1\): \(1 + \frac{dy}{dx} = 1\), so \(\frac{dy}{dx} = 0\).

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If \(y\) is a function of \(x\) and \(\log(x + y) = xy\) then the value of \(\left(\frac{dy}{dx}\right)\) at \(x = 0\) is _____

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