 Hello and welcome to the session. My name is Asha and I am going to help you with the following question that says, find the derivative of the following functions and 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. 8th one is AX plus B upon PX square plus QX plus R. So let us start with the solution and let us denote the given function by FX. So FX is equal to AX plus B upon PX square plus QX plus R. Now let us denote the numerator by U and the denominator of the given function by V. We have to find the derivative of the given function FX that is F dash X and this by the quotient rule of differentiation is equal to derivative of U dash into V minus U into derivative of V dash upon V square. Now let us substitute the values of U and V then simplify it further. So this is equal to derivative of U that is AX plus B into the function V which is PX square plus QX plus R minus U that is AX plus B into derivative of V that is PX square plus QX plus R. One in the denominator we have V square and V is PX square plus QX plus R. Now derivative of AX plus B is A since derivative of AX is A into 1 and derivative of constant that is B as we are given that B is a constant so it is derivative with respect to X is 0. Then we have PX square plus QX plus R minus AX plus B into derivative of PX square plus QX plus R is 2PX plus Q. So this derivative of PX square is 2 into P into X and derivative of QX is Q into 1 and derivative of R which is a constant with respect to X is 0 and the denominator we have PX square plus QX plus R whole square. Now let's open the brackets we have A PX square plus AQX plus AR minus 2APX square minus AQX minus 2VPX minus VQ and in the denominator we have PX square plus QX plus R whole square. Now APX square and minus 2APX square gives minus APX square. Then we have plus AQX and minus AQX on cancelling since they have opposite signs and we have minus 2BPX and plus AR minus BQ on PX square plus QX plus R whole square. This is our answer. Thus on differentiating the given function we get the derivative as minus APX square minus 2BPX plus AR minus BQ upon VX square plus QX plus R whole square. So this completes the session by intake queue.