Question

differentiate y=(x^2+1)sech(lnx) based on hyperbolic functions​

Answer 1

Answer:

The hyperbolic functions are defined as combinations of the exponential functions

e

x

and

e

−

x

.

The basic hyperbolic functions are the hyperbolic sine function and the hyperbolic cosine function. They are defined as follows:

sinh

x

=

e

x

−

e

−

x

2

,

cosh

x

=

e

x

+

e

−

x

2

.

The other hyperbolic functions

tanh

x

,

coth

x

,

sech

x

,

csch

x

are obtained from

sinh

x

and

cosh

x

in exactly the same way as the trigonometric functions

tan

x

,

cot

x

,

sec

x

and

csc

x

are defined in terms of

sin

x

and

cos

x

:

tanh

x

=

sinh

x

cosh

x

;

coth

x

=

cosh

x

sinh

x

(

x

≠

0

)

;

sech

x

=

1

cosh

x

;

csch

x

=

1

sinh

x

(

x

≠

0

Answer 2

Answer:

Already answered on another oage , have a Look. phoro also attached !