 Hello friends welcome to the session I am Malka. I am going to help you find dy by dx in the following that is x square plus xy plus y square equal to 100. So let's start with the solution. Our given equation is x square plus xy plus y square equal to 100. Now differentiate both sides with respect to x we get dy dx of x square plus dy dx of xy plus dy dx of y square equal to dy dx of 100. This is equal to dy dx of x square is 2x plus we apply the product rule in dy dx of xy which is first term into derivative of the second term that is dy dx of y plus second term into derivative of first term which is dy dx of x plus dy dx of y square is 2y into dy by dx which is equal to 0 since we all know that derivative of a constant is 0. So this can be written as 2x plus x into dy by dx plus y into 1 since derivative of x with respect to x is 1 plus 2y into dy by dx equal to 0. Now this can be written as 2x plus x into dy by dx plus y plus 2y into dy by dx equal to 0. So this is equal to now we will take dy by dx common and this will give us x plus 2y equal to minus 2x minus y therefore dy by dx equal to minus common 2x plus y upon x plus 2y therefore dy by dx equal to minus common 2x plus y upon x plus 2y which is a required solution hope you understood it I will enjoy the session goodbye and take care.