Find 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): `(p x^2+q x+r)/(a x+b)`

Explanation

let `f(x)=(px^2+qx+r)/(ax+b)`

Thus by quotient rule,

`f′(x)=((ax+b)d/(dx)(px^2+qx+r)−(px^2+qx+r)d/(dx)(ax+b))/(ax+b)^2`

= `((ax+b)(2px+q)−(px^2+qx+r)(a))/(ax+b)^2`

=`(apx^2+2bpx+bq−ar)/(ax+b)^2`

​