 Hello and welcome to the session. In this session we are going to discuss the following question. Differentiate 3 into x square plus y square whole square equal to minus 100 xy with respect to x. Here we are given the function 3 into x square plus y square whole square is equal to minus 100 xy. Now this is an implicit function so we use implicit differentiation to solve it. Differentiating both sides with respect to x we get d by dx of 3 into x square plus y square whole square is equal to d by dx of minus 100 xy. Now we use both power rule and product rule of differentiation and we get 3 into 2 into x square plus y square raise to power 2 minus 1 d by dx of x square plus y square is equal to minus 100 into x into d by by dx plus y into dx by dx. This implies 6 into x square plus y square the whole into 2x plus 2y d by by dx is equal to minus 100 into x d by by dx plus y. This implies 12 x cube plus 12 x square y d by by dx plus 12 x y square plus 12 y cube d by by dx is equal to minus 100 x d by by dx. Now keeping all terms of d by by dx on one side and bring all the other terms of the other side we get 12 x square y d by by dx plus 12 y cube d by by dx plus 100 x cube d by by dx plus 120 x cube d by by dx plus 120 x cube d by by dx. x dy by dx is equal to minus 100y minus 12x cube minus 12xy square. Now let us factor out dy by dx. We get 12x square y plus 12y cube plus 100x the whole into dy by dx is equal to minus 100y minus 12x cube minus 12xy square. This implies dy by dx is equal to minus 100y minus 12x cube minus 12xy square upon 12x square y plus 12y cube plus 100x. This is done on isolating dy by dx by dividing. Now four is common in both numerator and denominator that is dy by dx is equal to 4 into minus 25y minus 3x cube minus 3xy square upon 4 into 3x square y plus 3y cube plus 25x which implies dy by dx is equal to minus 25y minus 3x cube minus 3xy square upon 3x square y plus 3y cube plus 25x. This is the required answer. This completes our session. Hope you enjoyed the session.