 Hello friends welcome to the session I am Alka I am going to help you find dy by dx in y equal to sin inverse 1 minus x square upon 1 plus x square where 0 is less than x is less than 1. So let us start with the solution we are given y equal to sin 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 this implies y equal to sin inverse 1 minus 10 square theta upon 1 plus 10 square theta. Now since we all know that cos 2 theta equal to 1 minus 10 square theta upon 1 plus 10 square theta so this implies y equal to sin inverse cos 2 theta. Now we all know that sin 90 minus theta equal to cos theta therefore in place of cos 2 theta we will write y equal to sin inverse sin pi by 2 minus 2 theta this implies y equal to pi by 2 minus 2 theta and we can also say that y equal to pi by 2 minus 2 into 10 inverse x using equation first. Now we will differentiate both the sides with respect to x this gives us dy upon dx equal to dy upon dx of pi by 2 minus 2 into d of dx 10 inverse x 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.