Home » Page 13

Derivatives of hyperbolic functions

The derivatives of the hyperbolic functions are quite straightforward and somewhat analogous to the derivatives of their trigonometric counterparts. Here are the derivatives for the six primary hyperbolic functions: (1) Hyperbolic Sine $sinh$:$$\frac{d}{dx} \sinh(x) = \cosh(x)$$The derivative of hyperbolic sine is hyperbolic cosine. ProofThe hyperbolic sine and cosine functions are defined as follows: $$\sinh(x) =

Derivatives of hyperbolic functions Read More »

integration of hyperbolic functions

Integrating hyperbolic functions is similar to integrating their trigonometric counterparts, but there are some key differences due to the properties of hyperbolic functions. Here are the basic integrals for the six primary hyperbolic functions: (1) Sinh (Hyperbolic Sine):$$\int \sinh(x) \, dx = \cosh(x) + C$$The integral of hyperbolic sine is hyperbolic cosine. ProofTo integrate$\sinh(x)), we

integration of hyperbolic functions Read More »

Hyperbolic functions

Hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions. They are defined in terms of the exponential function and are important in many areas of mathematics, including algebra, geometry, calculus, and complex analysis. Hyperbolic functions are closely related to the exponential function, as evident from their definitions. The basic hyperbolic functions are: Definition

Hyperbolic functions Read More »