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Lesson 8

Differentiation of

Hyperbolic Functions

OBJECTIVES:

• to differentiate functions involving

hyperbolic functions;

• to solve problems involving differentiation

of hyperbolic functions; and

• to apply theorems to simplify the

functions.

DIFFERENTIATION FORMULA

Derivative of Hyperbolic

Function

A. Find the derivative of each of the following

functions and simplify the result:

1. y =sinh xcosh 2 x

y' coshx( sinh x cosh x )

y' sinhx( sinhxcoshx) coshx(cosh x sinh x)

y' sinhxsinh x cosh xcoshx

2 2

2 2

5

2 2

2 2 2

= +

= + +

= +

3. y sech x

2

y' =− 2 sechxsechxtanh x

2

2. y =lnsinh x

EXAMPLE

y' 2 sech xtanh x

2

2

2

sinhx

2 xcoshx

y' =

2

y' = 2 xcothx