If y = x+ x+ x+ + to then d y d x = - Vidyadip

MCQ

If $y =\sqrt{x+\sqrt{x+\sqrt{x+\ldots+\text { to }} \infty \infty}}$ then $\frac{d y}{d x}=$

A
$\frac{1}{2 y+1}$
✓
$\frac{1}{2 y-1}$
C
$\frac{x}{y+1}$
D
$\sqrt{\frac{x}{y+1}}$

✓

Answer

Correct option: B.

$\frac{1}{2 y-1}$

Explanation: $y =\sqrt{(x+y)}$
$y^2=x+y$
$2 yy^{\prime}=1+y^{\prime}$

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