Question

If $y=\frac{1}{\sqrt{x}},then\frac{dy}{dx}$=?

• A. $\frac{-1}{2x}$
• B. $\frac{-1}{2x^{\frac{3}{2}}}$
• C. $\frac{-1\sqrt{x}}{2}$
• D. None of these

Answer 1

The correct option is B

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

Differentiating both sides w.r.t. x,

$\frac{dy}{dx}=\frac{d\left[\right(x{)}^{\frac{-1}{2}}]}{dx}=-\frac{1}{2}{x}^{\frac{-3}{2}}=-\frac{1}{2x^{\frac{3}{2}}}$