 Hi and welcome to the session. Let's work out the following question. The question says if y is equal to x plus square root x squared plus a squared, the whole range to power n prove that dy by dx is equal to n y divided by square root of x squared plus y squared. Let us see the solution to this question. y is given to be x plus square root x squared plus a squared, the whole range to power n. So dy by dx will be equal to n into x plus square root x squared plus a squared, the whole range to power n minus 1 multiplied by derivative of this function. Now dy dx of x is 1 plus dy dx of square root x squared plus a squared case 1 upon 2 into square root x squared plus a squared into 2x this is equal to n into x plus square root x squared plus a squared, the whole range to power n multiplied by x plus square root x squared plus a squared raise to power minus 1 multiplied by 1 plus, now 2 gets cancelled with 2, so 1 plus x upon square root x squared plus a squared. This can be written further as now we see that this is same as y, so we can say this is n y multiplied by 1 upon x plus square root x squared plus a squared into 1 plus x in divided by square root x squared plus a squared this is equal to n y into 1 upon x plus square root x squared plus a squared plus x divided by square root x squared plus a squared into x plus square root x squared plus a squared. This is equal to n into y multiplied by square root x square plus a square plus x divided by x plus square root x square plus a square into square root x square plus a square. This is equal to ny into x plus square root x square plus a square divided by x plus square root x square plus a square into square root x square plus a square. This is equal to ny into, now this gets cancelled with this, so we have ny into 1 upon square root x square plus a square. So we can say that dy by dx is equal to ny divided by square root x square plus a square. So this is what we were supposed to prove in this question. I hope that you understood the solution and enjoyed the session. Have a good day.