Derivative of Inverse Tan

Determine the derivative of the following inverse trig function

$f(x) = \arctan{(\sqrt{x})}$

Determine the derivative of the inverse trigonometric function

$f(x) = \sec^{-1}{(5x)}$

Show that for $y = \cos^{-1}(x)$ the first derivative, $\frac{dy}{dx} = \frac{1}{x^2 + 1}$

For the following function, find the first derivative

$\theta = \frac{\tan^{-1}(2r)}{\pi{r}}$