DIFFERENTIATION OFINVERSE HYPERBOLIC

FUNCTIONS

TRANSCENDENTAL FUNCTIONS

Kinds of transcendental functions:1.logarithmic and exponential functions2.trigonometric and inverse trigonometric functions3.hyperbolic and inverse hyperbolic functions Note:Each pair of functions above is an inverse to each other.

DIFFERENTIATION FORMULA

Derivative of Inverse Hyperbolic Function

A. Find the derivative of each of the following functions and simplify the result:

EXAMPLE:

21 x1xsinhxxG .1

2

1

2 x12

x21xsinh1

x1

1xx'G

2

1

2 x1

xxsinh

1x

xx'G

xsinhx'G 1212 xcoshxy .2

x2xcoshx21x

1x'y 21

4

2

21

4

2

xcosh1x

xx2

21424

4

xcosh1xx1x

1xx2'y

xtanhx1xlny .3 12

1xtanh1x1

1x

1x2

x2

1x

1'y 1

222

xtanhx1

x

1x

x'y 1

22

xtanh'y 1

313 x31cothlogxF .4

313 x31cothlog

2

1xF 2

23331x9

x311

1elog

x31coth

1

2

1x'F

31633

2

x31cothx9x6112

elogx9x'F

31333

2

x31cothx32x32

elogx9x'F

3133

x31cothx32x2

elog3x'F

x4cothcothxG .5 1

x42

4x4hcsc

x4coth1

1x'G 2

2

x4hcscx4

x4hcsc2x'G

2

2

x

x

x2

2x'G

2

xhcscy .6

21

x22

1

2x

12x

1'y

222

442 x4x

4

4x4

x

x2'y

4

4

x4x

x44'y

A. Find the derivative and simplify the result.EXERCISES:

21 x3tansinhxf.1

x

1csccosh3xh.2 1

2x31 ecostanhy.3

2i x6hsechsecxg.4

21 xhsecy.5

2x95 esinhlogy.6

22 x31coshx31sinh3xh.7

xcoshxsinhxG.8

1x3cosh1

1x3sinhxH.9

3

x

1coshxF.10

2x5tanhlnxf.11