 Hi and welcome to the session. I am Shashi and I am going to help you with the following question. The question is, find the second order derivatives of the functions. The given function is tan inverse x. Let us start the solution now. First of all, we just assume y is equal to tan inverse x. Now, differentiating both sides with respect to x, we get dy by dx is equal to 1 upon 1 plus x square. Now, again differentiating both sides with respect to x, we get d square y upon dx square is equal to here we will apply the quotient rule to find the derivative. So, we will write 1 plus x square multiplied by derivative of 1 minus 1 multiplied by derivative of 1 plus x square upon 1 plus x square whole square. Now, this is equal to derivative of 1 is equal to 0. So, 0 multiplied by 1 plus x square is equal to 0. So, we get 0 minus derivative of 1 plus x square is equal to 0 plus 2x. So, we can say the derivative of 1 plus x square is equal to 2x. So, 2x multiplied by 1 is equal to 2x. So, we get 0 minus 2x upon 1 plus x square whole square. Or we can say the second derivative of y is equal to d square y upon dx square equal to minus 2x upon 1 plus x square whole square. So, our required second order derivative is minus 2x upon 1 plus x square whole square. This completes the session. Hope you understood the session. Take care and goodbye.