Question

If $y=\frac{2x-1}{x+2}$, then find $\frac{dy}{dx}$

Answer 1

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

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

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

$\frac{dy}{dx}=\frac{2x+4-2x+1}{(x+2{)}^2}$

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