Question

Differentiate the function $y=\frac{(x+2)(3x-1)}{(2x+5)}$ with respect to $x$

Answer 1

$y=\frac{(x+2)(3x-1)}{(2x+5)}$
$\frac{dy}{dx}=\frac{d}{dx}\frac{(x+2)(3x-1)}{(2x+5)}$
$=\frac{(2x+5)\frac{d}{dx}(x+2)(3x-1)-(x+2)(3x-1)\frac{d}{dx}(2x+5)}{(2x+5{)}^2}$
$=\frac{(2x+5)\left[\right(x+2\left)\frac{d}{dx}\right(3x-1)+(3x-1\left)\frac{d}{dx}\right(x+2\left)\right]-(x+2)(3x-1)[2+0]}{(2x+5{)}^2}$
$=\frac{(2x+5)\left[\right(x+2)\times 3+(3x-1)\times 1]-2[3x^2+6x-x-2]}{(2x+5{)}^2}$
$=\frac{(2x+5)[3x+6+3x-1]-6x^2-12x+2x+4}{(2x+5{)}^2}$
$=\frac{12x^2+30x+10x+25-6x^2-10x+4}{(2x+5{)}^2}$
$=\frac{6x^2+30x+29}{(2x+5{)}^2}$