Question

g(s)=root s-1/root s+1 by quotient rule
​

Answer 1

Answer:Explanation:

The quotient rule states that

d

d

x

(

f

g

)

=

f

'

g

−

f

g

'

g

2

Let's compute everything's required, and then we'll just substitute our results in this formula: we have

f

(

x

)

=

x

⇒

f

'

(

x

)

=

1

g

(

x

)

=

√

x

2

+

1

⇒

g

'

(

x

)

=

x

√

x

2

+

1

Also,  

g

2

(

x

)

=

x

2

+

1

Thus,

f

'

g

−

f

g

'

g

2

=

1

⋅

√

x

2

+

1

−

x

⋅

x

√

x

2

+

1

x

2

+

1

We can write this last result as

√

x

2

+

1

−

x

2

√

x

2

+

1

x

2

+

1

And then we can rearrange the numerator as

x

2

+

1

−

x

2

√

x

2

+

1

x

2

+

1

which equals

1

√

x

2

+

1

(

x

2

+

1

)

=

1

(

x

2

+

1

)

3

2

Explanation: