 Hi 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 derivatives of the functions. The given function is x cube multiplied by log x. Now let us start the solution. First you call let us assume y is equal to x cube multiplied by log x. Now differentiating both sides with respect to x we get dy upon dx is equal to x cube multiplied by derivative of log x plus log x multiplied by derivative of x cube. Now this is equal to x cube multiplied by 1 upon x plus log x multiplied by 3 x square. Now this further implies dy by dx is equal to x square plus 3 x square log x. Now let us name this equation as 1. Differentiating both sides of equation 1 with respect to x we get d square y upon dx square is equal to 2x plus 3x square multiplied by derivative of log x plus log x multiplied by derivative of x square multiplied by 3. Or we can say 3 log x multiplied by derivative of x square. Now clearly we can see d square y upon dx square is equal to 2x plus 3x square multiplied by 1 upon x plus 3 log x multiplied by 2x. Derivative of log x is 1 upon x derivative of x square is equal to 2x. So now second derivative of y is equal to 2x plus 3x plus xx log x. Or we can write d square y upon dx square is equal to 2x plus 3x is equal to 5x. 5x plus 6x log x or we can write d square y upon dx square is equal to x multiplied by 5 plus 6 log x. So our required second order derivative is given by x multiplied by 5 plus 6 log x. This is our required answer. This completes the session. Hope you understood the session. Take care and goodbye.