 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 log of log x. Let us start the solution now. First of all let us assume y is equal to log of log x. Now differentiating both sides with respect to x we get dy upon dx is equal to 1 upon log x multiplied by 1 upon x or we can say dy upon dx is equal to 1 upon x log x. Now again differentiating both sides with respect to x we get p square by upon dx square is equal to x log x multiplied by derivative of 1 minus 1 multiplied by derivative of x log x upon square of x log x. We have applied the quotient rule here. Now this is further equal to 0 minus 1 multiplied by derivative of x log x. Now derivative of x log x is equal to x multiplied by 1 upon x plus log x multiplied by 1 upon x log x whole square. Now this is further equal to x and x will get cancelled. Now it is equal to minus 1 multiplied by 1 plus log x upon x log x whole square. So the second order derivative of y is equal to minus 1 multiplied by 1 plus log x upon x log x square. Or we can write d square y upon dx square is equal to minus 1 plus log x upon log x whole square. So our required second derivative is 1 plus log x multiplied by negative sign upon square of x log x. This is our required answer. This completes the session. Hope you understood the session. Take care and goodbye.