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

If $y = t - \frac{1}{t}$ and $x = t + \frac{1}{t}$, then $\frac{dy}{dx}$ is equal to

If $e^y(x + 1) = 1$ and $\frac{d^2y}{dx^2} = k(\frac{dy}{dx})^2$, then k is equal to

If $y=\tan^{-1}(x+y)$, then $\frac{d^2y}{dx^2}$ is equal to:

If $x^2y^2 = a^{\pi/2}$, then $\dfrac{d^2y}{dx^2} =$

If the function $f(x)=\begin{cases}3x-6, & x \le 5 \\ 4k, & x>5\end{cases}$ is continuous at $x=5$, then the value of $k$ is:

Let

$f(x)=\begin{cases} |x|+3 & \text{if } x\le -3 \\ -2x & \text{if } -3<x<3 \\ 6x+2 & \text{if } x\ge 3 \end{cases}$

Then, which of the following is true?