 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 It is to be understood that A, B, C, D, P, Q, R and S affects non-zero constants and M and N are integers The fifth one is AX plus B upon CX plus D First let us learn the quotient rule Suppose we have two functions fx and gx which are real valued functions such that gx is not equal to 0 Then the derivative of the quotient of these two functions that is d dx of fx upon gx is equal to d dx of fx into gx minus fx into d dx of gx upon gx whole square So with the help of this rule we shall be finding the derivative of the given function that this is our P idea Let us now start with the solution Let us denote the given function by y So y is equal to AX plus B upon CX plus D We have to find its derivative that is dy upon dx So this by the quotient rule here let AX plus B be fx and CX plus D be gx Now let us apply the quotient rule to find the derivative of the given function First we have to find the derivative of fx which is AX plus B into gx that is CX plus D minus fx that is AX plus B into derivative of gx that is CX plus D Upon the denominator we have gx whole square and gx is here CX plus D so we have CX plus D whole square This is further equal to derivative of AX plus B is A since derivative of constant here B is the constant with respect to x is 0 and derivative of AX is A since derivative of x with respect to x is 1 and A into 1 is A into CX plus D minus AX plus B into derivative of CX plus D derivative of D is again 0 since it is a constant and derivative of CX is C Upon the denominator we have CX plus D whole square This is further equal to ACX plus AD minus ACX minus BC upon CX plus D whole square Now plus ACX cancels out with minus ACX and we have in the numerator AD minus BC upon CX plus D whole square Hence the derivative of the given function is AD minus BC upon CX plus D whole square This completes the session hope you have understood it well take care and have a good day