Question

If, $y=9\sqrt{x+\sqrt{x+\sqrt{x+....\infty }}}$ find $\left(\frac{dy}{dx}\right)$ at a point where y = 3.

• (A) 3
• (B) -3
• (C) -6
• (D) -9

Answer 1

The Correct Option is B

Explanation:
$y^2=9(x+y)$$2y\left(\frac{dy}{dx}\right)=9+9\left(\frac{dy}{dx}\right)$$\left(\frac{dy}{dx}\right)=\frac{9}{2y-9}$Now putting y = 3 we get $\left(\frac{dy}{dx}\right)=-3$Hence, the correct option is (B).