If $x = t^3$, $y = t^2$ then $\frac{d^2y}{dx^2}$ is equal to:

If $y = 500e^{7x} + 600e^{-7x}$, then $\frac{d^2y}{dx^2}$ equals :

If the function

$f(x) = \begin{cases} ax + 2, & x \leq 1 \\ x^2 + 3x + b, & x > 1 \end{cases}$

is differentiable at $x = 1$, then the value of $(2a + b)$ is

If $x = 3\sin\theta - \sin 3\theta$, $y = 3\cos\theta - \cos 3\theta$, then $\frac{d^2y}{dx^2}$ at $\theta = \frac{\pi}{3}$ is

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

If $y = \log_e \sin(e^x + 5x + 500)$ then $\dfrac{dy}{dx}$ is equal to

For $x > y > 0$, if $x^5 y^6 = (x + y)^{11}$, then $\frac{d^2y}{dx^2}$ is