Question

Solve $\frac{d}{dx}\left(\frac{1}{\sqrt{x}}\right)$

Answer 1

Given

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

Apply the power rule

$\frac{d}{dx}\left(x^a\right)=a{x}^{a-1}$

$\frac{d}{dx}\left(x^{\frac{-1}{2}}\right)=\frac{-1}{2}\left(x^{\frac{-1}{2}-1}\right)$

$=\frac{-1}{2}\left(x^{\frac{-3}{2}}\right)$

$=\frac{-1}{2x^{\frac{3}{2}}}$