Question

Differentiate $\frac{1}{\sqrt{x}}$ w.r.t $x$

Answer 1

Let $y=\frac{1}{\sqrt{x}}$

$\Rightarrow y=x^{\frac{-1}{2}}$

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

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