What is the value of $\frac{1}{2}$?

The value of $\frac{d}{dx}(\log_e x)$ is:

What is the value of $\alpha$ if $\alpha = \frac{25}{50}$?

$\int \frac{dx}{{(2ax - x^2)}^{1/2}} = a^n \sin^{-1} \left( \frac{x}{a} - 1 \right)$. In this formula,$n =$ . . . . . . .

What is the behavior of the magnitude of the slope of the shown graph?

Given that $y = \frac{10}{\sin x + \sqrt{3} \cos x}$. The minimum value of $y$ is