Math, asked by shivkumaryadav0843, 6 months ago

find the derivative of √ x with respect to x​

Answers

Answered by alpanag449
2

Answer:

Definition

f

'

(

x

)

=

lim

h

0

f

(

x

+

h

)

f

(

x

)

h

By Definition,

f

'

(

x

)

=

lim

h

0

x

+

h

x

h

by multiplying the numerator and the denominator by

x

+

h

+

x

,

=

lim

h

0

x

+

h

x

h

x

+

h

+

x

x

+

h

+

x

=

lim

h

0

x

+

h

x

h

(

x

+

h

+

x

)

by cancelling out

x

's and

h

's,

=

lim

h

0

1

x

+

h

+

x

=

1

x

+

0

+

x

=

1

2

x

Hence,

f

'

(

x

)

=

1

2

x

.

I hope that this was helpful.

Answered by 08416
0

Answer:

Step-by-step Convert the square root to its exponential form and then use the power rule.

y

=

x

=

x

1

2

Now bring the power of

1

2

down as a coefficient and then subtract 1 from the current power of

1

2

. Evaluate the fractions and simplify. Manipulate exponents from negative to positive.

y

'

=

1

2

x

(

1

2

1

)

=

1

2

x

(

1

2

2

2

)

=

1

2

x

(

1

2

)

=

1

2

x

1

2

=

1

2

x

:

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