Question

Find the derivative of the following functions (it is to be understood that a, b, c, d are fixed non-zero constants):
f(x)= $\frac{ax+b}{cx+d}$

Answer 1

Here $f\left(x\right)=\frac{ax+b}{cx+d}$

$\therefore f^{\prime }\left(x\right)=\frac{d}{dx}\left[\frac{ax+b}{cx+d}\right]$

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

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

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