Differentiate the following with respect of `x :(sqrtx+1/(sqrtx))^3""`

Explanation

Given `(sqrtx+1/(sqrtx))^3`

`=frac{d}{d x}[(sqrt{x})^{3}+3(sqrt{x})^{2}(frac{1}{sqrt{x}})+3(sqrt{x})(frac{1}{sqrt{x}})^{2}+(frac{1}{sqrt{x}})^{3}]`

`=frac{d}{d x}(x^{frac{3}{2}})+3 frac{d}{d x}(x^{frac{1}{2}})+3 frac{d}{d x}(x^{frac{-1}{2}})+frac{d}{d x}(x^{frac{-3}{2}})`

`=frac{3}{2} x^{frac{3}{2}}-1+3 cdot frac{1}{2} x^{frac{1}{2}}-1+3(frac{-1}{2}) x^{frac{-1}{2}}-1+(frac{-3}{2}) x^{frac{-3}{2}}-1`

`=frac{3}{2} x^{frac{1}{2}}+frac{3}{2} x^{frac{-1}{2}}-frac{3}{2} x^{frac{3}{2}}-frac{3}{2} x^{frac{-5}{2}}`