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Lesson 10 - Differentiation of Inverse Hyperbolic Functions, Slides of Calculus for Engineers

Definitions of inverse hyperbolic functions Derivative proofs Logarithmic forms Calculus applications Comparison with regular inverse functions

Typology: Slides

2024/2025

Available from 06/04/2025

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Lesson 10
Differentiation of
Inverse Hyperbolic
Functions
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Lesson 10

Differentiation of

Inverse Hyperbolic

Functions

OBJECTIVES

  • to apply the derivative formulas to solve for the

derivatives of inverse hyperbolic functions; and

  • to solve problems involving derivatives of

inverse hyperbolic functions.

Find the derivative of each of the following

functions and simplify the result:

EXAMPLE:

1 2

1. G x = xsinh x− 1 +x

( ) ( ) (^ )( ) 2

1 2 2 1 x

2 x 1 sinh x 1 1 x

1 G' x x

+ − 

  

=

( ) 2

1 2 1 x

x sinh x x 1

x G' x

=

G' ( )x sinh x

− 1

y x x x

2 1

2. ln 1 tanh

( ) 1 (tanh x)( ) 1 1 x

1 x

2 x 1

2 x

x 1

1 y'

1

2 2 2

− −

=

tanh x 1 x

x

x 1

x y'

1 2 2

=

y' tanh x

− 1