Let y = x , , + , , x , , + , ,x , , + , ,...... , , then dy dx = - Vidyadip

MCQ

Let y =$\sqrt {x\,\, + \,\,\sqrt {x\,\, + \,\,\sqrt {x\,\, + \,\,......\,\,\infty } } }$ then $\frac{{dy}}{{dx}}$ =

A
$\frac{1}{{2\,y\,\, - \,\,1}}$
B
$\frac{y}{{2x\,\, + \,\,y}}$
C
$\frac{1}{{\sqrt {1\,\, + \,\,4x} }}$
✓
All of the above

✓

Answer

Correct option: D.

All of the above

d
$y^2 = x + y ==>\frac{{dy}}{{dx}} =$$\frac{1}{{2\,y\,\, - \,\,1}}$

also $y =\frac{x}{y} + 1 $

$==>\frac{{dy}}{{dx}} =\frac{y}{{2\,x\,\, + \,\,y}}$

make a quadratic in $y$ to get explicit function $==> C$

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