Question

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):\(\frac{(ax+b)}{(cx+d)}\)

Answer 1

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