 Hello and welcome to the session. In this session, we discussed the following question which says, find dy by dx if x square plus y square, the whole square is equal to xy. Let's proceed with the solution now. We're given x square plus y square, the whole square is equal to xy. We need to find dy by dx. Now, let this be equation 1. Next, we differentiate equation 1. So, on differentiating 1 with respect to x, we get 2 into x square plus y square into dy by dx of x square plus dy dx of y square. This is equal to dy dx of xy. Further, we get 2 into x square plus y square and this whole multiplied by 2x plus 2y into dy by dx. And this is equal to, now we apply the product rule here. So, this would be equal to x into dy by dx plus y into 1. Now further, we have 4x into x square plus y square the whole plus 4y into x square plus y square the whole multiplied by dy by dx is equal to x into dy by dx plus y. Now we shift the term containing dy by dx from the right hand side to the left hand side. So, now we have 4x into x square plus y square the whole plus 4y into x square plus y square the whole multiplied by dy by dx minus x into dy by dx is equal to y. So, now we shift this term to the right hand side and further we get dy by dx this whole into 4y into x square plus y square the whole minus x is equal to y minus 4x into x square plus y square the whole. This further gives us dy by dx whole into 4x square y plus 4y cube minus x is equal to y minus 4x cube minus 4x y square. That is we now have dy by dx is equal to y minus 4x cube minus 4x y square this whole upon 4x square y plus 4y cube minus x. So, this is the final value for dy by dx this completes the session hope you have understood the solution of this question.