 Hello and welcome to the session. My name is Mansi and I'm going to help you with the following question. The question says find dy by dx when x and y are connected by the following relation that is log of under the root x square plus y square equal to tan inverse y by x. In this question we have to find dy by dx when x and y are connected by the following relation. So now let us start with a solution to this question. The relation given to us is log of under the root x square plus y square equal to tan inverse y by x. Now this is an implicit function and we have to find dy by dx for this function. So for this we differentiate equation 1 on both sides with respect to x. So we get d by dx of log of under the root x square plus y square equal to d by dx of tan inverse y by x. This implies 1 by under the root x square plus y square into d by dx of under the root x square plus y square equal to 1 by 1 plus y by x the whole square into d by dx of y by x. Now this further implies 1 divided by under the root x square plus y square into 1 by 2 into under the root x square plus y square into d by dx of x square plus y square equals to x square divided by x square plus y square into x into dy by dx minus y divided by x square. This implies 1 by 2 into x square plus y square into 2x plus 2y dy by dx is equal to x divided by x square plus y square into dy by dx minus y divided by x square plus y square. Now this implies 2x divided by 2 into x square plus y square plus 2y divided by 2 into x square plus y square into dy by dx minus x by x square plus y square into dy by dx equals to minus y divided by x square plus y square. This implies y by x square plus y square minus x by x square plus y square this whole multiplied by dy by dx equals to minus y by x square plus y square minus x by x square plus y square. This implies y minus x divided by x square plus y square this whole into dy by dx is equal to minus y minus x divided by x square plus y square. Now this implies dy by dx is equal to minus of x plus y divided by x square plus y square into x square plus y square divided by y minus x. This implies dy by dx is equal to minus of x plus y divided by minus of x minus y minus sign gets cancelled and we get x plus y divided by x minus y. So our answer to this question is x plus y divided by x minus y. So I hope you understood the question and enjoyed the session. Have a good day.