Question:medium

If $ y = \sqrt{\sin x + \sqrt{\sin x + \sqrt{\sin x + \cdots}}} $, then $ \frac{dy}{dx} $ is:

Show Hint

For $y = \sqrt{f(x) + \sqrt{f(x) + \dots}}$, the derivative is always $f'(x)/(2y-1)$.

Updated On: Apr 8, 2026

$\frac{\cos x}{2y-1}$
$\frac{\sin x}{2y-1}$
$\frac{\cos x}{y-1}$
$\frac{\sin x}{y-1}$

Show Solution

The Correct Option is A

Solution and Explanation

Was this answer helpful?

Questions Asked in MET exam

Let $ D = \begin{vmatrix} n & n^2 & n^3 \\ n^2 & n^3 & n^5 \\ 1 & 2 & 3 \end{vmatrix} $. Then $ \lim_{n \to \infty} \frac{M_{11} + C_{33}}{(M_{13})^2} $ is:

MET - 2024
Determinants

View Solution

Given vectors $\vec{a}, \vec{b}, \vec{c}$ are non-collinear and $(\vec{a}+\vec{b})$ is collinear with $(\vec{b}+\vec{c})$ which is collinear with $\vec{a}$, and $|\vec{a}|=|\vec{b}|=|\vec{c}|=\sqrt{2}$, find $|\vec{a}+\vec{b}+\vec{c}|$.

MET - 2024
Addition of Vectors

View Solution

Given $\frac{dy}{dx} + 2y\tan x = \sin x$, $y=0$ at $x=\frac{\pi}{3}$. If maximum value of $y$ is $1/k$, find $k$.

MET - 2024
Differential equations

View Solution

A real differentiable function $f$ satisfies $f(x)+f(y)+2xy=f(x+y)$. Given $f''(0)=0$, then \[ \int_0^{\pi/2} f(\sin x)\,dx = \]

MET - 2024
Definite Integral

View Solution

If \( y = \sqrt{\sin x + \sqrt{\sin x + \sqrt{\sin x + \cdots}}} \), then \( \frac{dy}{dx} \) is:

Show Hint

The Correct Option is A

Solution and Explanation

Top Questions on Continuity and differentiability

Questions Asked in MET exam