 Hello and welcome to the session, I am Shashi and I am going to help you with the following question. Question is, find the second order derivative of the functions, the given function is x multiplied by cos x. Let us start the solution now, first of all let us assume y is equal to x multiplied by cos x. Now differentiating both sides with respect to x we get T by upon dx is equal to x multiplied by the derivative of cos x plus cos x multiplied by derivative of x. Now this is equal to x multiplied by minus sin x plus cos x multiplied by 1. Now we get dy upon dx is equal to minus x sin x plus cos x. Now again differentiating both sides of equation 1 with respect to x we get T square y upon dx square is equal to minus x multiplied by cos x plus sin x multiplied by minus 1 plus minus sin x. So this implies T square by upon dx square is equal to minus x cos x minus sin x minus sin x. As we know sin x multiplied by minus 1 is equal to minus sin x and this is also equal to minus sin x and minus sin x minus sin x is equal to minus 2 sin x. So we get second derivative is equal to minus x cos x minus 2 sin x. So the required second order derivative is given by minus x cos x minus 2 sin x. This is our required answer. This completes the session. Hope you enjoyed the session. Goodbye.