Question

Differentiate $y=\frac{2x+5}{x+1}$ w.r.t $x$

Answer 1

$y=\frac{2x+5}{x+1}$

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

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

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

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