 Hello and welcome to the session. The question says, find the derivative of the following functions that 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. Ninth one is Px square plus Qx plus R upon Ax plus P. So let's start with the solution and let us denote the given function by Fx. So Fx is equal to Px square plus Qx plus R upon Ax plus P. Now let us denote the numerator of the given function by U and the denominator by V. We have to find the derivative of the given function that is F dash x and this is equal to derivative of U into V minus U into derivative of V upon V square. This is by the quotient rule of differentiation. Now let us put the values of U and V. So first we have to find the derivative of U that is ddx of U as Px square plus Qx plus R into V just Ax plus B and we have minus sign U U as Px square plus Qx plus R into derivative of V that is Ax plus P and the denominator we have V square that is Ax plus B whole square. Now simplifying it further derivative of Px square plus Qx plus R is 2 Px plus Q into Ax plus B minus Px square plus Qx plus R and the derivative of Px plus B is A. The denominator we have Ax plus B whole square. Now this is further equal to opening the brackets we have 2 Apx square Qx plus BQ minus Apx square minus Apx minus Ar upon Ax plus B whole square. Now 2 Apx square minus Apx square gives Apx square and we have plus 2 Bpx and plus Aqx cancels out with minus Aqx and we have plus BQ and minus Ar and the denominator we have Ax plus B whole square. Thus on differentiating the given function our answer is Apx square plus 2 Bpx plus Bq minus Ar upon Ax plus B whole square. So this completes the session by intake queue.