Question

Find the derivative of the following function (it is to be understood that $a,b,c,d,p,q,r$ and $s$ are fixed non-zero constants and $m$ and $n$ are integers) : $\frac{ax+b}{cx+d}$

Answer 1

Let, $f\left(x\right)=\frac{ax+b}{cx+d}$
Thus using quotient rule,
$f^{\prime }\left(x\right)=\frac{(cx+d)\frac{d(ax+b)}{dx}-(ax+b)\frac{d(cx+d)}{dx}}{(cx+d{)}^2}$
$=\frac{a(cx+d)-c(ax+b)}{(cx+d{)}^2}=\frac{ad-bc}{(cx+d{)}^2}$