If x y 0, x+y 0 and x^m y^n=(x+y)^ m+n , where m, n N , then d y d x is equal to

Step-by-step solution

Given, x^m y^n=(x+y)^ m+n On taking log on both sides, we get m x+n y=(m+n) (x+y) On differentiating w.r.t. x , we get array rlrl & & m x + n y d y d x & = m+n x+y (1+ d y d x ) & m x - m+n x+y & = d y d x ( m+n x+y - n y ) & & m y-n x x(x+y) & = d y d x [ m y-n x (x+y) y ] & & d y d x & = y x array