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# Find the derivative of the following functions ( 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 ) $\large\frac{ax+b}{cx+d}$

Can you answer this question?

Let $f(x) = \large\frac{ax+b}{cx+d}$
By quotient rule,
$f'(x) =\large\frac{(cx+d) \Large\frac{d}{dx}(ax+b) -(ax+b)\Large\frac{d}{dx}(cx+d)}{(cx+d)^2}$
$= \large\frac{(cx+d)(a)-(ax+b)(c)}{(cx+d)^2}$
$= \large\frac{acx+ad-acx-bc}{(cx+d)^2}$
$= \large\frac{ad-bc}{(cx+d)^2}$
answered Apr 12, 2014