 Hello and welcome to the session. The question says find the derivative of the following functions. It is to be understood that A, B, C, D, B, Q, R and S are fixed non-zero constants and M and N are integers. 16th one is cos x upon 1 plus sin x. So let's start with the solution and let us denote the given function by y. So y is cos x upon 1 plus sin x. Let us denote the numerator by u that is cos x and denominator by v that is 1 plus sin x. Now we have to find its derivative that is dy upon dx. This is equal to, by the quotient rule of differentiation, derivative of u into v minus u into derivative of v upon v square. Now this is further equal to u dash that is derivative of u dx of cos x into v 1 plus sin x minus u that is cos x into derivative of v that is 1 plus sin x. And in the denominator we have v square that is 1 plus sin x whole square. Now this is further equal to derivative of cos x with respect to x is minus sin x into 1 plus sin x minus cos x into derivative of 1 plus sin x is cos x upon 1 plus sin x whole square. This is further equal to minus sin x minus sin square x minus cos square x upon 1 plus sin x whole square. And this is further equal to minus sin x taking minus sin common from these two terms we have sin square x plus cos square x upon 1 plus sin x whole square. This is further equal to minus sin x minus 1 since sin square x plus cos square x is 1. Right and in the denominator we have 1 plus sin x whole square. Now this is further equal to taking minus sin common from the numerator we have 1 plus sin x upon 1 plus sin x whole square. Again on cancelling we have minus 1 upon 1 plus sin x. Thus on differentiating the given function we get the derivative as minus 1 upon 1 plus sin x. So this completes the session. Bye and take care.