Q.9 Find dy/dx , if √(x) + √(y) = √(a) .

Answer: dy/dx = -√(y/x) Differentiating both sides w.r.t. x : 1/2√(x) + 1/2√(y)dy/dx = 0 . therefore dy/dx = -2√(y)/2√(x) = -√(y)/√(x) .

Find \(\dfrac{dy}{dx}\), if \(\sqrt{x} + \sqrt{y} = \sqrt{a}\).

Q.9 Find \(\dfrac{dy}{dx}\), if \(\sqrt{x} + \sqrt{y} = \sqrt{a}\).

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

Best answer

Answer: \(\dfrac{dy}{dx} = -\sqrt{\dfrac{y}{x}}\)

Differentiating both sides w.r.t. \(x\): \(\dfrac{1}{2\sqrt{x}} + \dfrac{1}{2\sqrt{y}}\dfrac{dy}{dx} = 0\).

\(\therefore \dfrac{dy}{dx} = -\dfrac{2\sqrt{y}}{2\sqrt{x}} = -\dfrac{\sqrt{y}}{\sqrt{x}}\).

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

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