Question

Differentiate the following function w.r.t.x.
$\frac{1}{\sqrt{3x+7}}-\frac{1}{\sqrt{7-3x}}$

Answer 1

Consider given the given integration,

Let,

$y=\frac{1}{\sqrt{3x+7}}-\frac{1}{\sqrt{7-3x}}$

Differentiate with respect to x,

$\frac{d}{dx}y=\frac{d}{dx}\frac{1}{\sqrt{3x+7}}-\frac{d}{dx}\frac{1}{\sqrt{7-3x}}$

$\frac{dy}{dx}=\frac{-1}{2{(3x+7)}^{\frac{3}{2}}}.\frac{d}{dx}(3x+7)-\frac{(-1)}{2{(7-3x)}^{\frac{3}{2}}}.\frac{d}{dx}(7-3x)$

$\frac{dy}{dx}=\frac{-3}{2{(3x+7)}^{\frac{3}{2}}}-\frac{3}{2{(7-3x)}^{\frac{3}{2}}}$

Hence, this is the answer.