Question

Differentiate the following equation:
$(ax+b)/(cx+d)$

Answer 1

Let $y=\frac{ax+b}{cx+d}$

Differentiating y w.r.t. x, we get

$\frac{d}{dx}=\frac{(cx+d)\frac{d}{dx}(ax+b)-(ax+b)\frac{d}{dx}(cx+d)}{(cx+d{)}^2}$ (By quotient formula)

$=\frac{(cx+d)(a\times 1+0)-(ax+b)(c\times 1+0)}{(cx+d{)}^2}$

$=\frac{a(cx+d)-(ax+b)c}{(cx+d{)}^2}$

$=\frac{acx+ad-acx-bc}{(cx+d{)}^2}$

$\Rightarrow \frac{dy}{dx}=\frac{ad-bc}{(cx-d{)}^2}$