 Hello friends, welcome to the session I am Alka. I am going to help you find dy by dx in the following that is y equal to sin inverse 2x upon 1 plus x square. So let us start with the solution y equal to sin inverse 2x upon 1 plus x square. So let x equal to 10 theta which implies theta equal to 10 inverse x. Now we will substitute the value of x which is 10 theta in the given equation that is y equal to sin inverse 2 into 10 theta upon 1 plus 10 square theta. Now by using identity that is sin 2 theta equal to 2 10 theta upon 1 plus 10 square theta we get y equal to sin inverse sin 2 theta. Here we see that sin sin cancel out this implies y equal to 2 theta. Now this implies y equal to 2 into 10 inverse x. Now we will differentiate both the sides with respect to x we get dy by dx equal to 2 into dy by 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 into 1 upon 1 plus x square which is a required solution. Hope you understood it and enjoyed the session. Goodbye and take care.