derivatives of hyperbolic functions

In this entry we compute the derivative of the hyperbolic functionsDlmfMathworldPlanetmath sinh(x) and cosh(x).

Recall that by definition:

sinh(x) := ex-e-x2
cosh(x) := ex+e-x2.


ddxsinh(x) = ddx(ex-e-x2)
= 12ddx(ex-e-x)
= 12(ex-(-e-x))
= ex+e-x2
= cosh(x).

Similarly ddxcosh(x)=sinh(x). Using the quotient ruleMathworldPlanetmath, we compute the derivative of tanh(x)=sinh(x)cosh(x):


where we have used the equality cosh2(x)-sinh2(x)=1.

Title derivatives of hyperbolic functions
Canonical name DerivativesOfHyperbolicFunctions
Date of creation 2013-03-22 14:32:18
Last modified on 2013-03-22 14:32:18
Owner alozano (2414)
Last modified by alozano (2414)
Numerical id 5
Author alozano (2414)
Entry type Derivation
Classification msc 26A09