Question

Differentiate the following function w.r.t.$x$
${(\sqrt{x}+\frac{1}{\sqrt{x}})}^5$

Answer 1

$\frac{d}{dx}\left[{(\sqrt{x}+\frac{1}{\sqrt{x}})}^5\right]$

$=5(\frac{d}{dx}\left[\sqrt{x}\right]+\frac{d}{dx}\left[\frac{1}{\sqrt{x}}\right]){(\sqrt{x}+\frac{1}{\sqrt{x}})}^4$

$=5(\frac{1}{2}{x}^{\frac{1}{2}-1}+(-\frac{1}{2})x^{-\frac{1}{2}-1}){(\sqrt{x}+\frac{1}{\sqrt{x}})}^4$

$=5(\frac{1}{2\sqrt{x}}-\frac{1}{2x^{\frac{3}{2}}}){(\sqrt{x}+\frac{1}{\sqrt{x}})}^4$