 Hello friends, welcome to the session. I am Malka. I am going to help you find dy upon dx in y equal to sin inverse into 2x root 1 minus x square, where minus 1 by root 2 is less than x is less than 1 upon root 2. So, let us start with the solution y equal to sin inverse 2x into 1 minus x square. Now, let x equal to sin theta, this implies theta equal to sin inverse x. Now, this implies y equal to sin inverse into 2 sin theta into square root of 1 minus sin square theta. As we all know that 1 minus sin square theta is equal to cos square theta and 2 sin theta cos theta is equal to sin 2 theta. Now, we will use these two identities and this implies y equal to sin inverse 2 sin theta cos theta. This implies y equal to sin inverse sin 2 theta. This implies y equal to 2 theta. This implies y equal to 2 into sin inverse x by using our equation first. Now, we will differentiate both sides with respect to x. This implies dy by dx equal to 2 into d of dx of sin inverse x. This implies dy by dx equal to 2 into 1 upon square root of 1 minus x square as derivative of sin inverse x is 1 upon square root of 1 minus x square. Therefore, dy by dx equal to 2 upon square root of 1 minus x square. Hope you understood the solution and enjoyed the session. Goodbye and take care.