If $y = \tan^{-1}\sqrt{\dfrac{1 + \sin 2x}{1 - \sin 2x}}$, then $\dfrac{\text{d}y}{\text{d}x}$ at $x = \dfrac{\pi}{6}$ is

The derivative of $\sin\left(\log\left(\dfrac{x+3}{x}\right)\right)$ is

If $e^y + xy = e$, then the ordered pair $\left(\dfrac{\text{d}y}{\text{d}x}, \dfrac{\text{d}^2 y}{\text{d}x^2}\right)$ at $x = 0$ is equal to

If $y = \log x^x$, then the value of $\left(\dfrac{dy}{dx}\right)^2$ at $x = e^2$ is