We were introduced to hyperbolic functions in Introduction to Functions and Graphs, along with some of their basic properties. In this section, we look at differentiation and integration formulas for ...We were introduced to hyperbolic functions in Introduction to Functions and Graphs, along with some of their basic properties. In this section, we look at differentiation and integration formulas for the hyperbolic functions and their inverses.
This page discusses the hyperbolic secant function, \( \text{sech}(x) = \frac{1}{\cosh(x)} \), and its interrelations with other hyperbolic functions through key identities. It presents its derivative...This page discusses the hyperbolic secant function, \( \text{sech}(x) = \frac{1}{\cosh(x)} \), and its interrelations with other hyperbolic functions through key identities. It presents its derivatives, notably that the first derivative is \( \frac{d}{dx} \text{sech}(x) = -\tanh(x) \text{sech}(x) \), and highlights that the integral of \( \text{sech}(x) \) over its entire domain is equal to \( \pi \).
