Question

give correct answer with proper explanation ​

Answer 1

Answer:

OPTION 3) IS CORRECT.

$1 - \frac{1}{ {x}^{2} } .$

Explanation:

$\frac{d}{dx} {( \sqrt{x} + \frac{1}{ \sqrt{x} } )}^{2} = 2( \sqrt{x} + \frac{1}{ \sqrt{x} } ). \frac{d}{dx} ( \sqrt{x} + \frac{1}{ \sqrt{x} } ) \\ \\ = 2( \sqrt{x} + \frac{1}{ \sqrt{x} } )( \frac{1}{2 \sqrt{x} } - \frac{1}{2 x\sqrt{x} } ) \\ \\ = 2( \sqrt{x} + \frac{1}{ \sqrt{x} } ) \\ \\ = ( \sqrt{x} + \frac{1}{ \sqrt{x} } ). \frac{1}{ \sqrt{x} } (1 - \frac{1}{x} ) \\ \\ = (1 + \frac{1}{x} ).(1 - \frac{1}{x} ) \\ \\ = 1 - \frac{1}{ {x}^{2} } .$