If $y = ax^{n+1} + bx^{-n}$, then $x^2 \dfrac{d^2y}{dx^2}$ is equal to

If $y = \sqrt{2024x + 2025}$, then which of the following is correct?

If $y = \log_3(\log x)$, (Consider $\log_e x = \log x$) then the value of $\frac{dy}{dx}$ is

The second order derivative of which of the following functions is $5^{\mathrm{x}}$ ?

If $y = 3^x + e^x + x^x + x^3$, then the value of $\frac{dy}{dx}$ at $x = 3$ is

If the function defined by $f(x) = \begin{cases} \ kx^2 + 1, & \text{if } x \le 1 \\ 2 , & \text{if } x > 1 \end{cases}$ is continuous at $x = 1$, then k is equal to

For the function $f(x) = \sqrt{x}$, which of the following statements are true?

(A) $f(x)$ is continuous for $x \geq 0$.

(B) $f(x)$ is continuous for $x \in R$ (Set of real numbers).

(C) $f(x)$ is differentiable for $x > 0$.

(D) $f(x)$ is differentiable for $x \in R$ (Set of real numbers).

Choose the correct answer from the options given below: