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

If $y = \cos^{-1}(\sin x)$, where $\dfrac{\pi}{2} < x < \pi$, then $\dfrac{dy}{dx} = ...$