If , then is equal…

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

If y=x+y+x+y+…y=\sqrt{x+\sqrt{y+\sqrt{x+\sqrt{y+\dots}}}}, then dydx\frac{dy}{dx} is equal to (1) y+xy2−2x\frac{y+x}{y^2-2x} (2) y3−x2y2−2xy−1\frac{y^3-x}{2y^2-2xy-1} (3) y3+x2y2−x\frac{y^3+x}{2y^2-x} (4) None of these

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