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Mathematics Question on Limits and derivations

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

Answer

Let f(x)= (ax+b)(cx+d)\frac{(ax+b)}{(cx+d)}
By quotient rule,
f'(x)= (cx+d)ddx(ax+b)−(ax+b)ddx(cx+d)(cx+d)2\frac{(cx+d)\frac{d}{dx}(ax+b)-(ax+b)\frac{d}{dx}(cx+d)}{(cx+d)^2}
=(ex+d)(a)−(ax+b)(c)(cx+d)2\frac{(ex+d)(a)-(ax+b)(c)}{(cx+d)^2}
=acx+ad−acx−bc(cx+d)2\frac{acx+ad-acx-bc}{(cx+d)^2}
=ad−bc(cx+d)2\frac{ad-bc}{(cx+d)^2}