Calculus 1: Inverse and Hyperbolic Trig Derivatives

Find the derivative, $y^{\prime}$ of the following implicit function

$y = \tan^{-1}(xy)$

Show that $\frac{d}{dx}(\arcsin{x}) = \frac{x^{\prime}}{\sqrt{1 - x^2}}$

Determine the derivative of the following inverse trig function

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

Determine the derivative of the inverse trigonometric function

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

Find the derivative of $f(x) = 2\arccos{(\frac{x}{3})}$

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

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

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

Find the derivative of the following hyperbolic function

$f(x) = \sin{(\sinh{(x)})}$

Find the derivative of $f(x) = {(\sinh^{-1}(x))}^{\frac{3}{2}}$

Find the derivative of $\sinh{(x)}$ and $\cosh{(x)}$

Find the derivative of $\tanh{(3^{x^2} + 4x)}$