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):\(\frac{ax+b}{px^2+qx+r}\)

Answer 1

Let f (x)= \(\frac{ax+b}{px^2+qx+r}\)
By quotient rule,
f'(x)=- (px²+qx+r) \(\frac{d}{dx}\)(ax+b)-(ax+b) \(\frac{d}{dx}\)\(\frac{(px^2+qx+r)}{(px^2+qx+r)^2}\)
=(px²+qx+r)(a)-(ax+b) (2px + q) \(\frac{(px^2+qx+r)}{(px^2+qx+r)^2}\)