Inverse Trig Derivative Example

Determine the derivative of the following inverse trig function

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

Determine the derivative of the inverse trigonometric function

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

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

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

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