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Differentiate the following functions wi...

Differentiate the following functions with respect to `x :` `(sqrt(x)+1/(sqrt(x)))^2`

A

` ` `1-(1/(x))^2`

B

` ` `1+(1/(x))^2`

C

` ` `x-(1/(x))^2`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Let,y=`(sqrt(x)+1/(sqrt(x)))^2`
so` (dy/dx)=2(sqrt(x)+1/(sqrt(x)))[1/(2sqrt(x))-1/(2(x)^(3/2))]`
=`2(1/2-1/(2x)+1/(2x)-1/(2x^2))`
=`1-1/(x^2)`
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