List of top Mathematics Questions on Continuity and differentiability asked in MET

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

The function whose derivative is equal to itself is

The function \( f(x) = (x^2 - 1)|x^2 - 3x + 2| + \cos|x| \) is non-differentiable at

If $f(x+y)=f(x)f(y)$ for all $x,y$ and $f(15)=2,\ f'(0)=3$, then $f'(5)$ will be

Let \(A = \begin{bmatrix} 0 & \alpha \\ 0 & 0 \end{bmatrix}\) and \((A + I)^{50} - 50A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}\) then the value of \(a + b + c + d\) is

If \( Z = f(x + ay) + \phi(x - ay) \), then

\( y = e^{a \sin^{-1}(x)} \implies (1 - x^{2}) y_{n+2} - (2n+1)x y_{n+1} \) is equal to

If $y = \log(\log x)$, then $dy/dx$ is:

The derivative of \( e^{x^{3}} \) with respect to \( \log x \) is:

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

The function $f(x) = |x|$ is:

If $y = \log(\log x)$, then $dy/dx$ is: