Calculus - hyperbolic trigonometric

7/26/2019 Calculus - hyperbolic trigonometric

1/20

1

Week 7

Inverse trigonometric functions

Hyperbolic functions

Inverse hyperbolic functions


2/20

2Copyright Cengage Learning. ll rights reserve!.

6.6 Inverse "rigonometric #unctions


3/20

$

Inverse "rigonometric #unctions

"he !ifferentiation formulas for all of the inversetrigonometric functions.


4/20

%

&'ample 1

If f(x) * sin+1(x2+ 1), fin! f(x).

( ') *

f-(') * . ()

* . 2' *


5/20

&'ample 2

/ifferentiate (a) y*

0olution

y * ( ') *

y-

Chain rule


6/20

b) f(x) *x arctan

3ro!uct rule

' *

&'ample 2 (b). #in! f-(')


7/207

&'ercise 1

Calculate the !erivative of ()

' *


8/204

&'ercise 2

Calculate the !erivative of ' $'

( ') *

3ro!uct rule


9/20

5Copyright Cengage Learning. ll rights reserve!.

6.7 Hyperbolic #unctions


10/20

16

Hyperbolic #unctions

#or this reason they are collectively calle! hyperbolicfunctions an! in!ivi!ually calle! hyperbolic sine,

hyperbolic cosine, an! so on.


11/20

11


"he hyperbolic functions satisfy a number of i!entities thatare similar to ell8knon trigonometric i!entities.

We list some of them here.


12/20

12


"he !erivatives of the hyperbolic functions are easilycompute!. #or e'ample,


13/20

1$


We list the !ifferentiation formulas for the hyperbolicfunctions as "able 1.


14/20

1%

&'ample $

ny of these !ifferentiation rules can be combine! ith theChain 9ule. #or instance,


15/20

1

&'ercise $

y * . #in! y- :


16/20

1

&'ercise %

y * sin h (cosh '). #in! y- :


17/20

17

Inverse Hyperbolic #unctions


18/20

14

Inverse Hyperbolic #unctions

"he inverse hyperbolic functions are all !ifferentiablebecause the hyperbolic functions are !ifferentiable.


19/20

15

' *

0ho that ; (sin ')< * sec '

&'ample %


20/20

26

&'ercise

( ') *

Calculus - hyperbolic trigonometric

Documents

Transcript of Calculus - hyperbolic trigonometric