Derivative of ArcCos Example

Determine the derivative of the following inverse trig function

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

Determine the derivative of the inverse trigonometric function

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

Determine the derivative of $f(t) = \sin{(\arccos{(t)})}$

Let $f(x) = \tan{(x)}$ on the interval $\frac{-\pi}{2}$ < $x$ < $\frac{\pi}{2}$

What is $\frac{d}{dx}(\arctan{(x)})$ ?