 Hello friends welcome to the session I am Malka, I am going to help you find dy by dx in y equal to cos inverse 1 minus x square upon 1 plus x square where 0 is less than x is less than 1. Now let us start with the solution, we are given y equal to cos inverse 1 minus x square upon 1 plus x square. Now let us assume that x equal to 10 theta, this implies theta equal to 10 inverse x which is our first equation, this implies y equal to cos inverse 1 minus 10 square theta upon 1 plus 10 square theta, this implies y equal to cos inverse into cos 2 theta as cos 2 theta equal to 1 minus 10 square theta upon 1 plus 10 square theta, this implies y equal to cos inverse and cos 2 theta, this implies y equal to 2 theta. Now from our first equation we get y equal to 2 into 10 inverse x by using first equation. Now we differentiate both the sides with respect to x we get dy by dx equal to 2 into dy dx of 10 inverse x, this implies dy by dx equal to 2 into 1 upon 1 plus x square, therefore dy by dx equal to 2 upon 1 plus x square, hope you understood the solution and enjoyed the session goodbye and take care.