# Examples of Derivatives of Hyperbolic Functions

Example: Differentiate ${x^3}{\tanh ^2}\sqrt x$ 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

We have the given function

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