Question

Differentiate:$y=\frac{x+2}{3x+5}$ w.r.t $x$

Answer 1

$y=\frac{x+2}{3x+5}$

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

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

$\Rightarrow \frac{dy}{dx}=\frac{3x+5-3x-6}{{(3x+5)}^2}$

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