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

Answer: dy/dx = -√(x/y) The equation is x^(3/2) + y^(3/2) = a^(3/2) . Differentiating w.r.t. x : 3/2x^(1/2) + 3/2y^(1/2)dy/dx = 0 ⇒ dy/dx = -√(x)/√(y) = -√(x/y) .

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

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

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

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

The equation is \(x^{3/2} + y^{3/2} = a^{3/2}\). Differentiating w.r.t. \(x\):

\(\frac{3}{2}x^{1/2} + \frac{3}{2}y^{1/2}\frac{dy}{dx} = 0 \Rightarrow \frac{dy}{dx} = -\frac{\sqrt{x}}{\sqrt{y}} = -\sqrt{\frac{x}{y}}\).

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

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

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