# Examples of the Derivative of Inverse Hyperbolic Functions

Example: Differentiate ${\cosh ^{ - 1}}\left( {{x^2} + 1} \right)$ with respect to $x$.

Consider the function

Differentiating both sides with respect to $x$, we have

Using the product rule of differentiation, we have

Example: Find $\frac{{dy}}{{dx}}$ if the given function is $y = {\sinh ^{ - 1}}\left( {\coth {x^2}} \right)$

We have the given function

Differentiating both sides with respect to $x$, we have