 Hello friends welcome to the session I am Alka I am going to help you find dy by dxn y equal to cos inverse 2x upon 1 plus x square where minus 1 is less than x is less than 1. So let us start with the solution we are given y equal to cos inverse 2x upon 1 plus x square. Now let us assume that x equal to 10 theta this implies theta equal to 10 inverse x. Now this implies y equal to cos inverse 2 10 theta upon 1 plus 10 square theta this implies y equal to cos inverse into sin 2 theta as we know that sin 2 theta is equal to 210 theta upon 1 plus 10 square theta and this implies y equal to cos inverse cos 90 minus 2 theta which is equal to sin 2 theta. So this implies y equal to pi by 2 minus 2 theta we know that theta is equal to 10 inverse x this implies y equal to pi by 2 minus 2 into 10 inverse x using first. This implies now on taking differentiation both sides with respect to x we get dy by dx equal to d by dx of pi by 2 minus 2 into dy dx of 10 inverse x we get this implies dy by dx equal to 0 minus 2 into 1 upon 1 plus x square. Therefore dy by dx equal to minus 2 upon 1 plus x square. Hope you understood the solution and enjoyed the session goodbye and take care.