 Hello and welcome to the session. My name is Asha and I am going to help you with the following question. Let's say find the derivative of the following functions. 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. So the third question is px plus q into r upon x plus s. So let's start with the solution and let us denote the given function by y. So y is equal to p into x plus q into r upon x plus s. Now we shall find the derivative of y with the help of product rule. Suppose s function is u and s is v. Then y is equal to u into v. Then it's derivative y dash is equal to u v whole dash. With the help of product rule we have u into v dash plus u dash into v. That is first we will keep u as it is and find the derivative of v plus then we will find the derivative of u and keep v as it is. Now let us find dy by dx first derivative of y. This is equal to first u as it is. So we have px plus q into derivative of v that is d dx of r upon x plus s plus then derivative of u that is d dx of px plus q into v. That is r upon x plus s. This is further equal to px plus q into now r and s are constants. So we have to find the derivative of r upon x only since derivative of a constant is 0. So derivative of s with respect to x is 0 and now finding the derivative of r upon x cliffs are into derivative of 1 by x plus now let us find the derivative of px plus q with respect to x. Now derivative of constant is 0 so derivative of q is 0 and derivative of px is p times of d dx of x into r upon s sorry r upon x plus s. This is further equal to px plus q into r and derivative of 1 upon x with respect to x is minus 1 upon x square. Plus p derivative of x with respect to x is 1 and we have r upon x plus s and this is further equal to minus pxr upon x square minus qr upon x square plus p upon x plus ps. Now simplifying it further we have minus pr upon x minus qr upon x square plus pr upon x plus ps. Now minus pr upon x cancels out with plus pr upon x and we have minus qr upon x square plus ps. And hence on finding the derivative of the given function our answer is minus qr upon x square plus ps. So this completes the session have a good day.