Differentiate each of the functions with respect to $^{'} x^{'}$
$\frac{a x + b}{c x + d}$

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Solution

Let $f (x) = \frac{a x + b}{c x + d}$
diff above equation w.r.t x
$f^{'} (x) = \frac{(c x + d) (a) - (a x + b) (c)}{(c x + d)^{2}}$
$= \frac{a c x + a d - a c x - c b}{(c x + d)^{2}} = \frac{a d - c b}{(c x + d)^{2}}$

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