Question

derivative of 1 by root x​

Answer 1

Answer:

Let f(x)=1√x , then y=1uandu=x12 , since √x=x12 . This means we have to differentiate both functions and multiply them. Let's start with y . By the power rule y'=1×u0=1

Step-by-step explanation:

Let

f

(

x

)

=

1

√

x

, then

y

=

1

u

and

u

=

x

1

2

, since

√

x

=

x

1

2

.

Simplifying further, we have that

y

=

u

and

u

=

x

−

1

2

The chain rule states

d

y

d

x

=

d

y

d

u

×

d

u

d

x

This means we have to differentiate both functions and multiply them. Let's start with

y

.

By the power rule

y

'

=

1

×

u

0

=

1

.

Now for

u

:

Once again by the power rule we get:

u

'

=

−

1

2

×

x

−

1

2

−

1

u

'

=

−

1

2

x

−

3

2

u

'

=

−

1

2

√

x

3

f

'

(

x

)

=

y

'

×

u

'

f

'

(

x

)

=

1

×

−

1

2

√

x

3

f

'

(

x

)

=

−

1

2

√

x

3

Hopefully this helps

Answer 2

Answer:

derivative of 1/√x is -1/2x^ 3/2.