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) $\frac{(px^2+qx+r)}{(px^2+qx+r)^2}$