Question

Differentiate the following functions with respect to x: (x+1/x)(√x+1/√x) ​

Answer 1

Step-by-step explanation:

We have,

$y = (x + \frac{1}{x} )( \sqrt{x} + \frac{1}{ \sqrt{x} } )$

$= > y = x \sqrt{x} + \sqrt{x} + \frac{1}{ \sqrt{x} } + \frac{1}{x \sqrt{x} }$

$= > \frac{dy}{dx} = \frac{3}{2} ( {x})^{ \frac{1}{2} } + \frac{1}{2} (x)^{ - \frac{1}{2} } + ( - \frac{1}{2} ({x})^{ - \frac{3}{2} } ) + ( - \frac{3}{2} (x)^{ - \frac{5}{2} } )$

$= > \frac{dy}{dx} = \frac{3}{2} \sqrt{x} + \frac{1}{2 \sqrt{x} } - \frac{1}{2x \sqrt{x} } - \frac{3}{2 {x}^{2} \sqrt{x} }$