 Hello friends, welcome to the session I am at. I am going to help you find dy by dx in the following that is x cube plus x square y plus x y square plus y cube equal to 81. And let's start with the solution and given equation is x cube plus x square y plus x square plus y cube equal to 81. Now on differentiating both sides with respect to x we get dy dx of x cube plus dy dx of x square y plus dy dx of x y square plus dy dx of y cube equal to dy dx of 81. So this is equal to 3x square plus we will apply the product rule for dy dx of x square y which is first term into derivative of second term plus second term into derivative of first term. Now again we will apply the product rule for x y square which is first term into derivative of second term plus second term into derivative of first term of y cube is 3 y square into dy by dx equal to 0 since we know that the derivative of a constant is 0. So this is equal to 3x square plus x square into dy by dx plus y into 2x plus into 2y dy by dx plus y square into 1 plus 3 y square into 2y. plus 3y square into dy by dx equal to 0. This can be written as 3x square plus x square dy by dx plus 2xy plus 2xy into dy by dx plus y square plus 3y square dy by dx equal to 0. So this can be written as x square dy by dx plus 2xy dy by dx plus 3y square dy by dx equal to minus 3x square minus 2xy minus y square. Now on taking dy by dx common we get x square plus 2xy plus 3y square equal to minus common 3x square plus 2xy plus y square. This implies that dy by dx equal to minus 3x square plus 2xy plus y square upon x square plus 2xy plus 3y square. Therefore dy by dx equal to minus 3x square plus 2xy plus y square upon x square plus 2xy plus 3y square. So hope you understood the solution and enjoyed the session. Goodbye and take care.