Question

Differentiate

$\frac{1}{4}[\frac{1}{\sqrt{2x^2+5}}-\frac{1}{\sqrt{2x^2-3}}]$

Answer 1

Let

$y=\frac{1}{4}[\frac{1}{\sqrt{2x^2+5}}-\frac{1}{\sqrt{2x^2-3}}]$

Differentiate on both sides w.r.t x

$\frac{dy}{dx}=\frac{1}{4}[\frac{-1}{(2x^2+5{)}^{\frac{3}{2}}\times \left(2\right)}\times \frac{d}{dx}(2x^2+5)-\frac{1}{(2x^2-3{)}^{\frac{3}{2}}}\times \left(\frac{-1}{2}\right)\times \frac{d}{dx}(2x^2-3\left)\right]$

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

$\therefore \frac{dy}{dx}=\frac{x}{2}(\frac{1}{(2x^2-3{)}^{\frac{3}{2}}}-\frac{1}{2(2x^2+5{)}^{\frac{3}{2}}})$