Differentiate the following function with respect of `x :(a x+b)/(p x^2+q x+r)`

Explanation

Let,u = ax + b and `v = px^2 + qx + r`

∴ y = u/v
(du/dx)=a and (dv/dx)=2px+q

By quotient rule we have

`(dy/dx)=(v(du/dx)-u(dv/dx))/v^2`

thus putting the values we get

`(dy/dx)=(-apx^2-2bpx+ar-bq)/(px^2+qx+r)^2`