 Hello and welcome to the session, my name is Mansi and I am going to help you with the following question. The question says, for some constants a and b, find the derivative of x minus a divided by x minus b. Let us start with a solution to this question. First of all we see that quotient rule states that d by dx of fx by gx is equal to d by dx of fx into gx minus fx into d by dx of gx divided by gx the whole square. So here also we have a similar condition because in the numerator and denominator we have two functions. So let fx be x minus a and gx be x minus b. So that will be equal to in the denominator we will have the square of denominator of this function. In the numerator we will have gx into d by dx of fx minus fx into d by dx of gx. So let fx be equal to x minus a and gx be equal to x minus b. So applying quotient rule we will have d by dx of x minus a divided by x minus b will be equal to gx that is x minus b into d by dx of x minus a minus fx that is x minus a into d by dx of gx that is x minus b this whole divided by gx the whole square that is x minus b the whole square. This is equal to x minus b into d by dx of x minus a will be equal to d by dx of x minus d by dx of a. dx by dx will become 1. Derivative of a with respect to x will be 0 because that is a constant minus x minus a again we will have 1 minus 0 divided by x minus b the whole square. Now this can be written as x minus b minus x minus a becomes plus a divided by x minus b the whole square plus x gets cancelled with minus x we have a minus b divided by a minus b the whole square here we have x minus b the whole square. So our answer to this question is a minus b divided by x minus b the whole square. So this is our answer to the question I hope that you understood the question and enjoyed the session have a good day.