 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. 13th one is, a x plus b raised to the power n into c x plus d raised to the power n. Let's start with the solution and first let us denote the given function by y. So we have a x plus b raised to the power n into c x plus d raised to the power n. Now we have to find its derivative that is d by upon d x. Let this function be denoted by u and let us denote c x plus d raised to the power m by v. So derivative of y is equal to u into v is derivative of u into v plus u into derivative of v and this is by the product rule of differentiation. Now let us put the values of u and v. So first we have derivative of the function u which is a x plus b raised to the power n with respect to x into v which is c x plus d raised to the power m and we have plus u which is a x plus b raised to the power n into derivative of v that is d by x of c x plus d raised to the power m. This is further equal to derivative of a x plus b raised to the power n is n into a x plus b raised to the power n minus 1 into derivative of the function a x plus b then we have c x plus d raised to the power m then plus sign. Then we have a x plus b raised to the power n into now let us find the derivative of c x plus d raised to the power m which is m into c x plus d raised to the power m minus 1 into derivative of c x plus d and this is because derivative of a function x raised to the power n with respect to x is n into x raised to the power n minus 1 this can further written as now n into a x plus b raised to the power n minus 1 and derivative of a x plus b with respect to x is a since derivative of constant is 0 and derivative of a x is a into 1 and we have c x plus d raised to the power m plus a x plus b raised to the power n into m into c x plus d raised to the power m minus 1 into d dx of c x plus d is c now let us say a x plus b raised to the power n minus 1 and c x plus d raised to the power m minus 1 common so here I give a left with m into a into c x plus d and then this term we have left with m into c into a x plus b thus on differentiating the given function its derivative is a x plus b raised to the power n minus 1 into c x plus d raised to the power m minus 1 and since if suppose this whole term is suppose p and this is suppose whole term is q and p plus q can be written as q plus p so we have m c into a x plus b plus n e into c x plus d so this is our answer and this completes the session hope you have understood it take care and bye for now